B. The particulate nature of matter

Estimate the power input to the heating element. State an appropriate unit for your answer.

Outline whether your answer to (a) is likely to overestimate or underestimate the power input.

Discuss, with reference to the molecules in the liquid, the difference between milk at 11 °C and milk at 84 °C.

Describe one other method by which significant amounts of energy can be transferred from the pipe to the surroundings.

Two blocks, X and Y, are placed in contact with each other. Data for the blocks are provided.

X has a mass $m$. What is the mass of Y?

A.  $\frac{m}{4}$

B.  $m$

C.  $4 m$

D.  $6 m$

Estimate the average speed of the helium atoms in the container.

The mass of a helium atom is 6.6 × 10^-27 kg. Estimate the average speed of the helium atoms in the container.

Estimate the specific latent heat of vaporization of water. State an appropriate unit for your answer.

The heater is removed and a mass of 0.30 kg of pasta at −10 °C is added to the boiling water.

Determine the equilibrium temperature of the pasta and water after the pasta is added. Other heat transfers are negligible.

Specific heat capacity of pasta = 1.8 kJ kg⁻¹ K⁻¹
Specific heat capacity of water = 4.2 kJ kg⁻¹ K⁻¹

A mass $m$ of a liquid of specific heat capacity $c$ flows every second through a heater of power $P$. What is the difference in temperature between the liquid entering and leaving the heater?

A.  $\frac{mc}{P}$

B.  $273+\frac{mc}{P}$

C.  $\frac{P}{mc}$

D.  $273+\frac{P}{mc}$

The mass of the wire is 18 g. The specific heat capacity of copper is 385 J kg⁻¹ K⁻¹. Estimate the increase in temperature of the wire.

A liquid of mass m and specific heat capacity c cools. The rate of change of the temperature of the liquid is k. What is the rate at which thermal energy is transferred from the liquid?

A. $\frac{mc}{k}$

B. $\frac{k}{mc}$

C. $\frac{1}{kmc}$

D. kmc

The temperature of a fixed mass of an ideal gas changes from 200 °C to 400 °C.

What is $\frac{\text{mean kinetic energy of gas at 200 °C}}{\text{mean kinetic energy of gas at 400 °C}}$?

A. 0.50

B. 0.70

C. 1.4

D. 2.0

A bicycle of mass $M$ comes to rest from speed $v$ using the back brake. The brake has a specific heat capacity of $c$ and a mass $m$. Half of the kinetic energy is absorbed by the brake.

What is the change in temperature of the brake?

A.  $\frac{M{v}^2}{4mc}$

B.  $\frac{M{v}^2}{2mc}$

C.  $\frac{m{v}^2}{4Mc}$

D.  $\frac{m{v}^2}{2Mc}$

A mass $m$ of water is at a temperature of 290 K. The specific heat capacity of water is $c$. Ice, at its melting point, is added to the water to reduce the water temperature to the freezing point. The specific latent heat of fusion for ice is $L$. What is the minimum mass of ice that is required?

A. $\frac{17mc}{L}$

B. $\frac{290mc}{L}$

C. $\frac{17mL}{c}$

D. $\frac{290mL}{c}$

A black-body radiator emits a peak wavelength of ${\lambda }_{\text{max}}$ and a maximum power of $P_0$. The peak wavelength emitted by a second black-body radiator with the same surface area is $2 {\lambda }_{\text{max}}$. What is the total power of the second black-body radiator?

A.  $\frac{1}{16}{P}_0$

B.  $\frac{1}{2}{P}_0$

C.  $2P_0$

D.  $16P_0$

Calculate the thermal energy transferred from the sample during the first $30$ minutes.

Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate unit for your answer.

Calculate the mass of the oil that remains unfrozen after $60$ minutes.

A piece of metal at a temperature of $100 °\text{C}$ is dropped into an equal mass of water at a temperature of $15 °\text{C}$ in a container of negligible mass. The specific heat capacity of water is four times that of the metal. What is the final temperature of the mixture?

A.  $83 °\text{C}$

B.  $57 °\text{C}$

C.  $45 °\text{C}$

D.  $32 °\text{C}$

When 40 kJ of energy is transferred to a quantity of a liquid substance, its temperature increases by 20 K. When 600 kJ of energy is transferred to the same quantity of the liquid at its boiling temperature, it vaporizes completely at constant temperature. What is

$\frac{\text{specific latent heat of vaporization}}{\text{specific heat capacity of the liquid}}$

for this substance?

A. 15 K⁻¹

B. 15 K

C. 300 K⁻¹

D. 300 K

An insulated tube is filled with a large number n of lead spheres, each of mass m. The tube is inverted s times so that the spheres completely fall through an average distance L each time. The temperature of the spheres is measured before and after the inversions and the resultant change in temperature is ΔT.

What is the specific heat capacity of lead?

A. $\frac{sgL}{nm\mathrm{\Delta }T}$

B. $\frac{sgL}{\mathrm{\Delta }T}$

C. $\frac{sgL}{n\mathrm{\Delta }T}$

D. $\frac{gL}{m\mathrm{\Delta }T}$

An insulated container of negligible mass contains a mass 2M of a liquid. A piece of a metal of mass M is dropped into the liquid. The temperature of the liquid increases by 10 °C and the temperature of the metal decreases by 80 °C in the same time.

What is $\frac{\text{specific heat capacity of the liquid}}{\text{specific heat capacity of the metal}}$?

A.  2

B.  4

C.  8

D.  16

A light source of power P is observed from a distance $d$. The power of the source is then halved.

At what distance from the source will the intensity be the same as before?

A.  $\frac{d}{\sqrt{2}}$

B.  $\frac{d}{2}$

C.  $\frac{d}{4}$

D.  $\frac{d}{8}$

Three statements about Boltzmann’s constant k_B are:

I.   k_B has a unit of J K⁻¹

II.  k_B $=\frac{\text{gas constant}}{\text{Avogadro's constant}}$

III. k_B $=\frac{\text{the average kinetic energy of particles}}{\text{temperature of the gas}}$

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Determine the minimum area of the solar heating panel required to increase the temperature of all the water in the tank to 30°C during a time of 1.0 hour.

The electromagnetic spectrum radiated by a black body at temperature T shows a peak at wavelength $\lambda$_p.

What is the variation of $\lambda$_p with T?

Planet $\text{X}$ and planet $\text{Y}$ both emit radiation as black bodies. Planet $\text{Y}$ has twice the surface temperature and one third of the radius of planet $\text{X}$.

What is $\frac{\text{power radiated by planet X}}{\text{power radiated by planet Y}}$? 

A.  $\frac{9}{16}$

B.  $\frac{3}{4}$

C.  $\frac{4}{3}$

D.  $\frac{16}{9}$

Three samples of the same liquid are mixed in an insulated container. The masses and initial temperatures of the samples are:

What is the equilibrium temperature of the mixture?

A.  45 °C

B.  36 °C

C.  30 °C

D.  24 °C

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Show that the surface temperature of δ Vel A is about 9000 K.

Calculate the theoretical equilibrium temperature of the mixture.

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Show that the surface temperature of δ Vel A is about 9000 K.

Calculate the theoretical equilibrium temperature of the mixture.

Window 1 is made of a single glass pane of thickness d. Window 2 is made of two glass panes of thickness d each, separated by a thin air space. Both windows have the same surface area and separate air masses of the same temperature difference.

Thermal energy transferred in unit time through window 1 is $Q$. The thermal energy transferred in unit time through window 2 is

A.  less than $\frac{Q}{2}$

B.  equal to $\frac{Q}{2}$

C.  between $\frac{Q}{2}$ and $Q$

D.  equal to $2Q$

A cylindrical metal rod has a temperature difference between its ends and is in a steady state. The rate of energy transfer along the rod is $P$. No energy is transferred from the curved side of the rod.

The rod is changed for one made from the same material but with double the length and double the diameter. The temperature difference is halved. The rate of energy transfer in the rod is now

A.  $\frac{P}{2}$

B.  $P$

C.  $2P$

D.  $4P$

Two ideally lagged bars have the same length and are made from the same metal. The diameters of the bars are different. One end of each bar is held at 100 °C and the other end is held at 0 °C.

For each bar

A.  the rate of energy transfer is the same

B.  the temperature gradient is the same

C.  the temperature gradient is non-linear

D.  the temperature gradient $\propto \frac{1}{{\text{bar diameter}}^2}$

Show that the average rate at which thermal energy is transferred into the chocolate is about 15 W.

Estimate the specific latent heat of fusion of chocolate.

Show that the average rate at which thermal energy is transferred into the chocolate is about 15 W.

Estimate the specific latent heat of fusion of chocolate.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

The temperature of an object is changed from θ₁ °C to θ₂ °C. What is the change in temperature measured in kelvin?

A.  (θ₂ − θ₁)

B.  (θ₂ − θ₁) + 273

C.  (θ₂ − θ₁) − 273

D.  273 − (θ₂ − θ₁)

A metal cube X of length L is heated gaining thermal energy Q. Its temperature rises by ΔT. A second cube Y, of length 2L, made of the same material, gains thermal energy of 2Q.

What is the temperature rise of Y?

A.  $\frac{\mathrm{\Delta }T}{8}$

B.  $\frac{\mathrm{\Delta }T}{4}$

C.  $\mathrm{\Delta }T$

D.  $2\mathrm{\Delta }T$

The temperature of an object is changed from θ₁ °C to θ₂ °C. What is the change in temperature measured in kelvin?

A.  (θ₂ − θ₁)

B.  (θ₂ − θ₁) + 273

C.  (θ₂ − θ₁) − 273

D.  273 − (θ₂ − θ₁)

Explain why star B has a greater surface area than star A.

Calculate, in m, the distance to star X.

Determine the ratio $\frac{\mathrm{luminosity} \mathrm{of} \mathrm{star} \mathrm{X}}{\mathrm{luminosity} \mathrm{of} \mathrm{star} \mathrm{Y}}$.

Explain why star B has a greater surface area than star A.

There are eight wheels on each tram with a brake system for each wheel. A pair of brake pads clamp firmly onto an annulus made of steel.

The train comes to rest from speed v. Ignore the energy transferred to the brake pads and the change in the gravitational potential energy of the tram during the braking.

Calculate the temperature change in each steel annulus as the tram comes to rest.

Data for this question                

The inner radius of the annulus is 0.40 m and the outer radius is 0.50 m.

The thickness of the annulus is 25 mm.

The density of the steel is 7860 kg m⁻³

The specific heat capacity of the steel is 420 J kg⁻¹ K⁻¹

The electrical power rating of the hot plate is 1 kW. Comment, with reference to this value, on your answer in (a)(ii).

the initial temperature gradient through the base of the pot. State an appropriate unit for your answer.

The temperature of the air outside of the bottle is 20 °C. The surface area of the bottle is 4.0 × 10⁻² m². Calculate the initial rate of thermal energy transfer by conduction through the bottle.

Explain why the rate calculated in part (a) is decreasing.

Estimate the initial rate of the change of the temperature of the water in the bottle. State your answer in K s⁻¹. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹.

The liquid now freezes so that the vertical column is entirely of ice. Suggest how your answer to (a)(ii) will change.

Calculate the temperature at Y.

The temperatures are now reversed so that X is at 45 °C and Z is at 90 °C. Show that the rate of energy transfer is unchanged.

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Calculate the theoretical equilibrium temperature of the mixture.

Show that the surface temperature of δ Vel A is about 9000 K.

Estimate the power input to the heating element. State an appropriate unit for your answer.

Outline whether your answer to (a) is likely to overestimate or underestimate the power input.

Discuss, with reference to the molecules in the liquid, the difference between milk at 11 °C and milk at 84 °C.

Describe one other method by which significant amounts of energy can be transferred from the pipe to the surroundings.

Estimate the power input to the heating element. State an appropriate unit for your answer.

Outline whether your answer to (a) is likely to overestimate or underestimate the power input.

Discuss, with reference to the molecules in the liquid, the difference between milk at 11 °C and milk at 84 °C.

Describe one other method by which significant amounts of energy can be transferred from the pipe to the surroundings.

Two blocks, X and Y, are placed in contact with each other. Data for the blocks are provided.

X has a mass $m$. What is the mass of Y?

A.  $\frac{m}{4}$

B.  $m$

C.  $4 m$

D.  $6 m$

Estimate the average speed of the helium atoms in the container.

Estimate the average speed of the helium atoms in the container.

The mass of a helium atom is 6.6 × 10^-27 kg. Estimate the average speed of the helium atoms in the container.

The mass of a helium atom is 6.6 × 10^-27 kg. Estimate the average speed of the helium atoms in the container.

Estimate the specific latent heat of vaporization of water. State an appropriate unit for your answer.

The heater is removed and a mass of 0.30 kg of pasta at −10 °C is added to the boiling water.

Determine the equilibrium temperature of the pasta and water after the pasta is added. Other heat transfers are negligible.

Specific heat capacity of pasta = 1.8 kJ kg⁻¹ K⁻¹
Specific heat capacity of water = 4.2 kJ kg⁻¹ K⁻¹

Estimate the specific latent heat of vaporization of water. State an appropriate unit for your answer.

The heater is removed and a mass of 0.30 kg of pasta at −10 °C is added to the boiling water.

Determine the equilibrium temperature of the pasta and water after the pasta is added. Other heat transfers are negligible.

Specific heat capacity of pasta = 1.8 kJ kg⁻¹ K⁻¹
Specific heat capacity of water = 4.2 kJ kg⁻¹ K⁻¹

A mass $m$ of a liquid of specific heat capacity $c$ flows every second through a heater of power $P$. What is the difference in temperature between the liquid entering and leaving the heater?

A.  $\frac{mc}{P}$

B.  $273+\frac{mc}{P}$

C.  $\frac{P}{mc}$

D.  $273+\frac{P}{mc}$

The mass of the wire is 18 g. The specific heat capacity of copper is 385 J kg⁻¹ K⁻¹. Estimate the increase in temperature of the wire.

The mass of the wire is 18 g. The specific heat capacity of copper is 385 J kg⁻¹ K⁻¹. Estimate the increase in temperature of the wire.

A liquid of mass m and specific heat capacity c cools. The rate of change of the temperature of the liquid is k. What is the rate at which thermal energy is transferred from the liquid?

A. $\frac{mc}{k}$

B. $\frac{k}{mc}$

C. $\frac{1}{kmc}$

D. kmc

The temperature of a fixed mass of an ideal gas changes from 200 °C to 400 °C.

What is $\frac{\text{mean kinetic energy of gas at 200 °C}}{\text{mean kinetic energy of gas at 400 °C}}$?

A. 0.50

B. 0.70

C. 1.4

D. 2.0

A bicycle of mass $M$ comes to rest from speed $v$ using the back brake. The brake has a specific heat capacity of $c$ and a mass $m$. Half of the kinetic energy is absorbed by the brake.

What is the change in temperature of the brake?

A.  $\frac{M{v}^2}{4mc}$

B.  $\frac{M{v}^2}{2mc}$

C.  $\frac{m{v}^2}{4Mc}$

D.  $\frac{m{v}^2}{2Mc}$

A mass $m$ of water is at a temperature of 290 K. The specific heat capacity of water is $c$. Ice, at its melting point, is added to the water to reduce the water temperature to the freezing point. The specific latent heat of fusion for ice is $L$. What is the minimum mass of ice that is required?

A. $\frac{17mc}{L}$

B. $\frac{290mc}{L}$

C. $\frac{17mL}{c}$

D. $\frac{290mL}{c}$

A black-body radiator emits a peak wavelength of ${\lambda }_{\text{max}}$ and a maximum power of $P_0$. The peak wavelength emitted by a second black-body radiator with the same surface area is $2 {\lambda }_{\text{max}}$. What is the total power of the second black-body radiator?

A.  $\frac{1}{16}{P}_0$

B.  $\frac{1}{2}{P}_0$

C.  $2P_0$

D.  $16P_0$

Calculate the thermal energy transferred from the sample during the first $30$ minutes.

Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate unit for your answer.

Calculate the mass of the oil that remains unfrozen after $60$ minutes.

Calculate the thermal energy transferred from the sample during the first $30$ minutes.

Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate unit for your answer.

Calculate the mass of the oil that remains unfrozen after $60$ minutes.

A piece of metal at a temperature of $100 °\text{C}$ is dropped into an equal mass of water at a temperature of $15 °\text{C}$ in a container of negligible mass. The specific heat capacity of water is four times that of the metal. What is the final temperature of the mixture?

A.  $83 °\text{C}$

B.  $57 °\text{C}$

C.  $45 °\text{C}$

D.  $32 °\text{C}$

When 40 kJ of energy is transferred to a quantity of a liquid substance, its temperature increases by 20 K. When 600 kJ of energy is transferred to the same quantity of the liquid at its boiling temperature, it vaporizes completely at constant temperature. What is

$\frac{\text{specific latent heat of vaporization}}{\text{specific heat capacity of the liquid}}$

for this substance?

A. 15 K⁻¹

B. 15 K

C. 300 K⁻¹

D. 300 K

An insulated tube is filled with a large number n of lead spheres, each of mass m. The tube is inverted s times so that the spheres completely fall through an average distance L each time. The temperature of the spheres is measured before and after the inversions and the resultant change in temperature is ΔT.

What is the specific heat capacity of lead?

A. $\frac{sgL}{nm\mathrm{\Delta }T}$

B. $\frac{sgL}{\mathrm{\Delta }T}$

C. $\frac{sgL}{n\mathrm{\Delta }T}$

D. $\frac{gL}{m\mathrm{\Delta }T}$

An insulated container of negligible mass contains a mass 2M of a liquid. A piece of a metal of mass M is dropped into the liquid. The temperature of the liquid increases by 10 °C and the temperature of the metal decreases by 80 °C in the same time.

What is $\frac{\text{specific heat capacity of the liquid}}{\text{specific heat capacity of the metal}}$?

A.  2

B.  4

C.  8

D.  16

A light source of power P is observed from a distance $d$. The power of the source is then halved.

At what distance from the source will the intensity be the same as before?

A.  $\frac{d}{\sqrt{2}}$

B.  $\frac{d}{2}$

C.  $\frac{d}{4}$

D.  $\frac{d}{8}$

Three statements about Boltzmann’s constant k_B are:

I.   k_B has a unit of J K⁻¹

II.  k_B $=\frac{\text{gas constant}}{\text{Avogadro's constant}}$

III. k_B $=\frac{\text{the average kinetic energy of particles}}{\text{temperature of the gas}}$

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Determine the minimum area of the solar heating panel required to increase the temperature of all the water in the tank to 30°C during a time of 1.0 hour.

Determine the minimum area of the solar heating panel required to increase the temperature of all the water in the tank to 30°C during a time of 1.0 hour.

The electromagnetic spectrum radiated by a black body at temperature T shows a peak at wavelength $\lambda$_p.

What is the variation of $\lambda$_p with T?

Planet $\text{X}$ and planet $\text{Y}$ both emit radiation as black bodies. Planet $\text{Y}$ has twice the surface temperature and one third of the radius of planet $\text{X}$.

What is $\frac{\text{power radiated by planet X}}{\text{power radiated by planet Y}}$? 

A.  $\frac{9}{16}$

B.  $\frac{3}{4}$

C.  $\frac{4}{3}$

D.  $\frac{16}{9}$

Three samples of the same liquid are mixed in an insulated container. The masses and initial temperatures of the samples are:

What is the equilibrium temperature of the mixture?

A.  45 °C

B.  36 °C

C.  30 °C

D.  24 °C

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Show that the surface temperature of δ Vel A is about 9000 K.

Show that the surface temperature of δ Vel A is about 9000 K.

Calculate the theoretical equilibrium temperature of the mixture.

Calculate the theoretical equilibrium temperature of the mixture.

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Show that the surface temperature of δ Vel A is about 9000 K.

Show that the surface temperature of δ Vel A is about 9000 K.

Calculate the theoretical equilibrium temperature of the mixture.

Calculate the theoretical equilibrium temperature of the mixture.

Window 1 is made of a single glass pane of thickness d. Window 2 is made of two glass panes of thickness d each, separated by a thin air space. Both windows have the same surface area and separate air masses of the same temperature difference.

Thermal energy transferred in unit time through window 1 is $Q$. The thermal energy transferred in unit time through window 2 is

A.  less than $\frac{Q}{2}$

B.  equal to $\frac{Q}{2}$

C.  between $\frac{Q}{2}$ and $Q$

D.  equal to $2Q$

A cylindrical metal rod has a temperature difference between its ends and is in a steady state. The rate of energy transfer along the rod is $P$. No energy is transferred from the curved side of the rod.

The rod is changed for one made from the same material but with double the length and double the diameter. The temperature difference is halved. The rate of energy transfer in the rod is now

A.  $\frac{P}{2}$

B.  $P$

C.  $2P$

D.  $4P$

Two ideally lagged bars have the same length and are made from the same metal. The diameters of the bars are different. One end of each bar is held at 100 °C and the other end is held at 0 °C.

For each bar

A.  the rate of energy transfer is the same

B.  the temperature gradient is the same

C.  the temperature gradient is non-linear

D.  the temperature gradient $\propto \frac{1}{{\text{bar diameter}}^2}$

Show that the average rate at which thermal energy is transferred into the chocolate is about 15 W.

Estimate the specific latent heat of fusion of chocolate.

Show that the average rate at which thermal energy is transferred into the chocolate is about 15 W.

Estimate the specific latent heat of fusion of chocolate.

Show that the average rate at which thermal energy is transferred into the chocolate is about 15 W.

Estimate the specific latent heat of fusion of chocolate.

Show that the average rate at which thermal energy is transferred into the chocolate is about 15 W.

Estimate the specific latent heat of fusion of chocolate.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

The temperature of an object is changed from θ₁ °C to θ₂ °C. What is the change in temperature measured in kelvin?

A.  (θ₂ − θ₁)

B.  (θ₂ − θ₁) + 273

C.  (θ₂ − θ₁) − 273

D.  273 − (θ₂ − θ₁)

A metal cube X of length L is heated gaining thermal energy Q. Its temperature rises by ΔT. A second cube Y, of length 2L, made of the same material, gains thermal energy of 2Q.

What is the temperature rise of Y?

A.  $\frac{\mathrm{\Delta }T}{8}$

B.  $\frac{\mathrm{\Delta }T}{4}$

C.  $\mathrm{\Delta }T$

D.  $2\mathrm{\Delta }T$

The temperature of an object is changed from θ₁ °C to θ₂ °C. What is the change in temperature measured in kelvin?

A.  (θ₂ − θ₁)

B.  (θ₂ − θ₁) + 273

C.  (θ₂ − θ₁) − 273

D.  273 − (θ₂ − θ₁)

Explain why star B has a greater surface area than star A.

Calculate, in m, the distance to star X.

Determine the ratio $\frac{\mathrm{luminosity} \mathrm{of} \mathrm{star} \mathrm{X}}{\mathrm{luminosity} \mathrm{of} \mathrm{star} \mathrm{Y}}$.

Explain why star B has a greater surface area than star A.

There are eight wheels on each tram with a brake system for each wheel. A pair of brake pads clamp firmly onto an annulus made of steel.

The train comes to rest from speed v. Ignore the energy transferred to the brake pads and the change in the gravitational potential energy of the tram during the braking.

Calculate the temperature change in each steel annulus as the tram comes to rest.

Data for this question                

The inner radius of the annulus is 0.40 m and the outer radius is 0.50 m.

The thickness of the annulus is 25 mm.

The density of the steel is 7860 kg m⁻³

The specific heat capacity of the steel is 420 J kg⁻¹ K⁻¹

There are eight wheels on each tram with a brake system for each wheel. A pair of brake pads clamp firmly onto an annulus made of steel.

The train comes to rest from speed v. Ignore the energy transferred to the brake pads and the change in the gravitational potential energy of the tram during the braking.

Calculate the temperature change in each steel annulus as the tram comes to rest.

Data for this question                

The inner radius of the annulus is 0.40 m and the outer radius is 0.50 m.

The thickness of the annulus is 25 mm.

The density of the steel is 7860 kg m⁻³

The specific heat capacity of the steel is 420 J kg⁻¹ K⁻¹

the initial temperature gradient through the base of the pot. State an appropriate unit for your answer.

The electrical power rating of the hot plate is 1 kW. Comment, with reference to this value, on your answer in (a)(ii).

The electrical power rating of the hot plate is 1 kW. Comment, with reference to this value, on your answer in (a)(ii).

the initial temperature gradient through the base of the pot. State an appropriate unit for your answer.

The temperature of the air outside of the bottle is 20 °C. The surface area of the bottle is 4.0 × 10⁻² m². Calculate the initial rate of thermal energy transfer by conduction through the bottle.

Explain why the rate calculated in part (a) is decreasing.

Estimate the initial rate of the change of the temperature of the water in the bottle. State your answer in K s⁻¹. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹.

The temperature of the air outside of the bottle is 20 °C. The surface area of the bottle is 4.0 × 10⁻² m². Calculate the initial rate of thermal energy transfer by conduction through the bottle.

Explain why the rate calculated in part (a) is decreasing.

Estimate the initial rate of the change of the temperature of the water in the bottle. State your answer in K s⁻¹. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹.

The liquid now freezes so that the vertical column is entirely of ice. Suggest how your answer to (a)(ii) will change.

The liquid now freezes so that the vertical column is entirely of ice. Suggest how your answer to (a)(ii) will change.

Calculate the temperature at Y.

The temperatures are now reversed so that X is at 45 °C and Z is at 90 °C. Show that the rate of energy transfer is unchanged.

Calculate the temperature at Y.

The temperatures are now reversed so that X is at 45 °C and Z is at 90 °C. Show that the rate of energy transfer is unchanged.

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Calculate the theoretical equilibrium temperature of the mixture.

Show that the surface temperature of δ Vel A is about 9000 K.

The missing section of insulation is 0.56 m long and the external radius of the pipe is 0.067 m. The emissivity of the pipe surface is 0.40. Determine the energy lost every second from the pipe surface. Ignore any absorption of radiation by the pipe surface.

The diagram shows, for a region on the Earth’s surface, the incident, radiated and reflected intensities of the solar radiation.

What is the albedo of the region?

A.  $\frac{1}{4}$

B.  $\frac{1}{3}$

C.  $\frac{3}{4}$

D.  $1$

A black body is on the Moon’s surface at point A. Show that the maximum temperature that this body can reach is 400 K. Assume that the Earth and the Moon are the same distance from the Sun.

The albedo of the Earth’s atmosphere is 0.28. Outline why the maximum temperature of a black body on the Earth when the Sun is overhead is less than that at point A on the Moon.

The average temperature of the surface of a planet is five times greater than the average temperature of the surface of its moon. The emissivities of the planet and the moon are the same. The average intensity radiated by the planet is $I$. What is the average intensity radiated by its moon?

A.  $\frac{I}{25}$

B.  $\frac{I}{125}$

C.  $\frac{I}{625}$

D.  $\frac{I}{3125}$

A black body at temperature T emits radiation with peak wavelength ${\lambda }_{\text{ρ}}$ and power P. What is the temperature of the black body and the power emitted for a peak wavelength of $\frac{{\lambda }_{\text{ρ}}}{2}$?

Show that the intensity of the solar radiation at the location of Titan is 16 W m⁻²

Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the average intensity of solar radiation absorbed by the whole surface of Titan is 3.1 W m⁻²

Estimate, in °C, the temperature of the roof tiles.

Two surfaces X and Y emit radiation of the same surface intensity. X emits a radiation of peak wavelength twice that of Y.

What is $\frac{\mathrm{emissivity} \mathrm{of} \mathrm{X}}{\mathrm{emissivity} \mathrm{of} \mathrm{Y}}$?

A.  $\frac{1}{16}$

B.  $\frac{1}{2}$

C.  2

D.  16

Two surfaces X and Y emit radiation of the same surface intensity. X emits a radiation of peak wavelength twice that of Y.

What is $\frac{\mathrm{emissivity} \mathrm{of} \mathrm{X}}{\mathrm{emissivity} \mathrm{of} \mathrm{Y}}$?

A.  $\frac{1}{16}$

B.  $\frac{1}{2}$

C.  2

D.  16

Light of intensity 500 W m⁻² is incident on concrete and on snow. 300 W m⁻² is reflected from the
concrete and 400 W m⁻² is reflected from the snow.

What is $\frac{\mathrm{albedo} \mathrm{of} \mathrm{concrete}}{\mathrm{albedo} \mathrm{of} \mathrm{snow}}$?

A.  $\frac{1}{2}$

B.  $\frac{3}{4}$

C.  $\frac{4}{3}$

D.  2

The missing section of insulation is 0.56 m long and the external radius of the pipe is 0.067 m. The emissivity of the pipe surface is 0.40. Determine the energy lost every second from the pipe surface. Ignore any absorption of radiation by the pipe surface.

The missing section of insulation is 0.56 m long and the external radius of the pipe is 0.067 m. The emissivity of the pipe surface is 0.40. Determine the energy lost every second from the pipe surface. Ignore any absorption of radiation by the pipe surface.

The diagram shows, for a region on the Earth’s surface, the incident, radiated and reflected intensities of the solar radiation.

What is the albedo of the region?

A.  $\frac{1}{4}$

B.  $\frac{1}{3}$

C.  $\frac{3}{4}$

D.  $1$

A black body is on the Moon’s surface at point A. Show that the maximum temperature that this body can reach is 400 K. Assume that the Earth and the Moon are the same distance from the Sun.

The albedo of the Earth’s atmosphere is 0.28. Outline why the maximum temperature of a black body on the Earth when the Sun is overhead is less than that at point A on the Moon.

A black body is on the Moon’s surface at point A. Show that the maximum temperature that this body can reach is 400 K. Assume that the Earth and the Moon are the same distance from the Sun.

The albedo of the Earth’s atmosphere is 0.28. Outline why the maximum temperature of a black body on the Earth when the Sun is overhead is less than that at point A on the Moon.

The average temperature of the surface of a planet is five times greater than the average temperature of the surface of its moon. The emissivities of the planet and the moon are the same. The average intensity radiated by the planet is $I$. What is the average intensity radiated by its moon?

A.  $\frac{I}{25}$

B.  $\frac{I}{125}$

C.  $\frac{I}{625}$

D.  $\frac{I}{3125}$

A black body at temperature T emits radiation with peak wavelength ${\lambda }_{\text{ρ}}$ and power P. What is the temperature of the black body and the power emitted for a peak wavelength of $\frac{{\lambda }_{\text{ρ}}}{2}$?

Show that the intensity of the solar radiation at the location of Titan is 16 W m⁻²

Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the average intensity of solar radiation absorbed by the whole surface of Titan is 3.1 W m⁻²

Show that the intensity of the solar radiation at the location of Titan is 16 W m⁻²

Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the average intensity of solar radiation absorbed by the whole surface of Titan is 3.1 W m⁻²

Estimate, in °C, the temperature of the roof tiles.

Estimate, in °C, the temperature of the roof tiles.

Two surfaces X and Y emit radiation of the same surface intensity. X emits a radiation of peak wavelength twice that of Y.

What is $\frac{\mathrm{emissivity} \mathrm{of} \mathrm{X}}{\mathrm{emissivity} \mathrm{of} \mathrm{Y}}$?

A.  $\frac{1}{16}$

B.  $\frac{1}{2}$

C.  2

D.  16

Two surfaces X and Y emit radiation of the same surface intensity. X emits a radiation of peak wavelength twice that of Y.

What is $\frac{\mathrm{emissivity} \mathrm{of} \mathrm{X}}{\mathrm{emissivity} \mathrm{of} \mathrm{Y}}$?

A.  $\frac{1}{16}$

B.  $\frac{1}{2}$

C.  2

D.  16

Light of intensity 500 W m⁻² is incident on concrete and on snow. 300 W m⁻² is reflected from the
concrete and 400 W m⁻² is reflected from the snow.

What is $\frac{\mathrm{albedo} \mathrm{of} \mathrm{concrete}}{\mathrm{albedo} \mathrm{of} \mathrm{snow}}$?

A.  $\frac{1}{2}$

B.  $\frac{3}{4}$

C.  $\frac{4}{3}$

D.  2

A quantity of an ideal gas is at a temperature T in a cylinder with a movable piston that traps a length L of the gas. The piston is moved so that the length of the trapped gas is reduced to $\frac{5L}{6}$ and the pressure of the gas doubles.

What is the temperature of the gas at the end of the change?

A.  $\frac{5}{12}T$

B.  $\frac{3}{5}T$

C.  $\frac{5}{3}T$

D.  $\frac{12}{5}T$

Calculate the number of gas particles in the cylinder.

An ideal gas is maintained at a temperature of 100 K. The variation of the pressure P and $\frac{1}{\text{volume}}$ of the gas is shown.

What is the quantity of the gas?

A.  $\frac{2\times {10}^5}{R} \text{mol}$

B.  $\frac{200}{R} \text{mol}$

C.  $\frac{80}{R} \text{mol}$

D.  $\frac{4}{5R} \text{mol}$

Cylinder X has a volume $V$ and contains 3.0 mol of an ideal gas. Cylinder Y has a volume $\frac{V}{2}$ and contains 2.0 mol of the same gas.

The gases in X and Y are at the same temperature $T$. The containers are joined by a valve which is opened so that the temperatures do not change.

What is the change in pressure in X?

A. $+\frac{1}{3}\left(\frac{RT}{V}\right)$

B. $-\frac{1}{3}\left(\frac{RT}{V}\right)$

C. $+\frac{2}{3}\left(\frac{RT}{V}\right)$

D. $-\frac{2}{3}\left(\frac{RT}{V}\right)$

Two flasks P and Q contain an ideal gas and are connected with a tube of negligible volume compared to that of the flasks. The volume of P is twice the volume of Q.

P is held at a temperature of 200 K and Q is held at a temperature of 400 K.

What is mass of $\frac{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{P}}{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{Q}}$?

A. $\frac{1}{8}$

B. $\frac{1}{4}$

C. 4

D. 8

The molar mass of an ideal gas is $M$. A fixed mass $m$ of the gas expands at a constant pressure $p$. The graph shows the variation with temperature T of the gas volume V.

What is the gradient of the graph?

A.  $\frac{Mp}{mR}$

B.  $\frac{MR}{mp}$

C.  $\frac{mp}{MR}$

D.  $\frac{mR}{Mp}$

A container holds 20 g of argon-40(${}_{18}^{40}\text{Ar}$)  and 40 g of neon-20 (${}_{10}^{20}\text{Ne}$) .

What is$\frac{\text{number of atoms of argon -40}}{\text{number of atoms of neon -20}}$ in the container?

A. 0.25

B. 0.5

C. 2

D. 4

The molar mass of helium is 4.0 g mol^-1. Show that the mass of a helium atom is 6.6 × 10^-27 kg.

Show that the number of helium atoms in the container is about 4 × 10²⁰.

Calculate the ratio  $\frac{\text{total volume of helium atoms}}{\text{volume of helium gas}}$.

Explain, using your answer to (d)(i) and with reference to the kinetic model, why this sample of helium can be assumed to be an ideal gas.

Show that the number of helium atoms in the container is 4 × 10²⁰.

Calculate the ratio $\frac{\text{volume of helium atoms}}{\text{volume of helium gas}}$.

Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.

The molar mass of water is 18 g mol⁻¹. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

A fixed mass of an ideal gas has a volume of $V$, a pressure of p and a temperature of $30 °\text{C}$. The gas is compressed to the volume of $\frac{V}{6}$ and its pressure increases to 12p. What is the new temperature of the gas?

A.  $15 °\text{C}$

B.  $60 °\text{C}$

C.  $333 °\text{C}$

D.  $606 °\text{C}$

The equation $\frac{pV}{T}$ = constant is applied to a real gas where p is the pressure of the gas, V is its volume and T is its temperature.

What is correct about this equation?

A. It is empirical.

B. It is theoretical.

C. It cannot be tested.

D. It cannot be disproved.

A gas storage tank of fixed volume V contains N molecules of an ideal gas at temperature T. The pressure at kelvin temperature T is 20 MPa. $\frac{N}{4}$ molecules are removed and the temperature changed to 2T. What is the new pressure of the gas?

A. 10 MPa

B. 15 MPa

C. 30 MPa

D. 40 MPa

Two containers X and Y are maintained at the same temperature. X has volume $4 {\mathrm{m}}^3$ and Y has volume $6 {\mathrm{m}}^3$. They both hold an ideal gas. The pressure in X is $100 \mathrm{Pa}$ and the pressure in Y is $50 \mathrm{Pa}$. The containers are then joined by a tube of negligible volume. What is the final pressure in the containers?

A.  $70 \mathrm{Pa}$

B.  $75 \mathrm{Pa}$

C.  $80 \mathrm{Pa}$

D.  $150 \mathrm{Pa}$

Two identical containers X and Y each contain an ideal gas. X has N molecules of gas at an absolute temperature of T and Y has 3N molecules of gas at an absolute temperature of $\frac{T}{2}$ What is the ratio of the pressures $\frac{P_Y}{P_X}$?

A.   $\frac{1}{6}$

B.   $\frac{2}{3}$

C.   $\frac{3}{2}$

D.   $6$

A substance in the gas state has a density about $1000$ times less than when it is in the liquid state. The diameter of a molecule is $d$. What is the best estimate of the average distance between molecules in the gas state?

A.  $d$

B.  $10d$

C.  $100d$

D.  $1000d$

A sample of oxygen gas with a volume of $3.0 {\text{m}}^3$ is at $100 °\text{C}$. The gas is heated so that it expands at a constant pressure to a final volume of $6.0 {\text{m}}^3$. What is the final temperature of the gas?

A. $750 °\text{C}$

B. $470 °\text{C}$

C. $370 °\text{C}$

D. $200 °\text{C}$

Three statements about Boltzmann’s constant k_B are:

I.   k_B has a unit of J K⁻¹

II.  k_B $=\frac{\text{gas constant}}{\text{Avogadro's constant}}$

III. k_B $=\frac{\text{the average kinetic energy of particles}}{\text{temperature of the gas}}$

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

The water is heated. Explain why the quantity of air in the storage tank decreases.

Gases in the atmosphere are compounds of ${}_6{}^{12}\text{C}$, ${}_1{}^1\text{H}$, ${}_8{}^{16}\text{O}$ and ${}_7{}^{14}\text{N}$.

Four of these gases are CO₂, N₂O, CH₄ and H₂O. A pure sample of each gas is produced. Each sample has the same mass.

Which sample contains the greatest number of molecules?

A.  N₂O

B.  H₂O

C.  CO₂

D.  CH₄

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

A sample of a gas has volume $V$ and contains $N$ molecules, each of mass $m$. The average translational speed of the molecules is $u$.

Which expression is equivalent to the pressure of the gas?

A.  $\frac{1}{3}\frac{NV}{m}{u}^2$

B.  $\frac{1}{3}\frac{Nm}{V}{u}^2$

C.  $\frac{1}{3}\frac{N}{mV}{u}^2$

D.  $\frac{1}{3}\frac{m}{NV}{u}^2$

Calculate the maximum temperature of the gas during the cycle.

Determine, using the graph, whether the gas acts as an ideal gas.

Calculate, in g, the mass of the gas.

Determine, using the graph, whether the gas acts as an ideal gas.

Calculate, in g, the mass of the gas.

A vessel contains a mass X of helium gas and a mass 2X of oxygen gas.

Molar mass of helium = 4 g

Molar mass of oxygen = 32 g

What is the $\frac{\mathrm{number} \mathrm{of} \mathrm{helium} \mathrm{atoms}}{\mathrm{number} \mathrm{of} \mathrm{oxygen} \mathrm{molecules}}$?

A.  $\frac{1}{8}$

B.  $\frac{1}{4}$

C.  4

D.  8

Discuss how the motion of the molecules of a gas gives rise to pressure in the gas.

The average speed of the molecules of a gas is 500 m s⁻¹. The density of the gas is 1.2 kg m⁻³. Calculate, in kPa, the pressure of the gas.

Calculate the average translational speed of air molecules.

The air is a mixture of nitrogen, oxygen and other gases. Explain why the component gases of air in the container have different average translational speeds.

The temperature of the sample is increased without a change in pressure. Outline the effect it has on the density of the gas.

the ideal gas law,

the kinetic energy of particles in an ideal gas.

A container holds a mixture of argon and helium atoms at a temperature of 37 °C.

Calculate the average translational speed of the argon atoms.

The molar mass of argon is 4.0 × 10⁻² kg mol⁻¹.

Calculate the pressure of the gas in the container.

Determine the mass of the gas in the container.

Calculate the average translational speed of the gas particles.

The temperature of the gas in the container is increased.

Explain, using the kinetic theory, how this change leads to a change in pressure in the container.

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

A quantity of an ideal gas is at a temperature T in a cylinder with a movable piston that traps a length L of the gas. The piston is moved so that the length of the trapped gas is reduced to $\frac{5L}{6}$ and the pressure of the gas doubles.

What is the temperature of the gas at the end of the change?

A.  $\frac{5}{12}T$

B.  $\frac{3}{5}T$

C.  $\frac{5}{3}T$

D.  $\frac{12}{5}T$

Calculate the number of gas particles in the cylinder.

Calculate the number of gas particles in the cylinder.

An ideal gas is maintained at a temperature of 100 K. The variation of the pressure P and $\frac{1}{\text{volume}}$ of the gas is shown.

What is the quantity of the gas?

A.  $\frac{2\times {10}^5}{R} \text{mol}$

B.  $\frac{200}{R} \text{mol}$

C.  $\frac{80}{R} \text{mol}$

D.  $\frac{4}{5R} \text{mol}$

Cylinder X has a volume $V$ and contains 3.0 mol of an ideal gas. Cylinder Y has a volume $\frac{V}{2}$ and contains 2.0 mol of the same gas.

The gases in X and Y are at the same temperature $T$. The containers are joined by a valve which is opened so that the temperatures do not change.

What is the change in pressure in X?

A. $+\frac{1}{3}\left(\frac{RT}{V}\right)$

B. $-\frac{1}{3}\left(\frac{RT}{V}\right)$

C. $+\frac{2}{3}\left(\frac{RT}{V}\right)$

D. $-\frac{2}{3}\left(\frac{RT}{V}\right)$

Two flasks P and Q contain an ideal gas and are connected with a tube of negligible volume compared to that of the flasks. The volume of P is twice the volume of Q.

P is held at a temperature of 200 K and Q is held at a temperature of 400 K.

What is mass of $\frac{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{P}}{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{Q}}$?

A. $\frac{1}{8}$

B. $\frac{1}{4}$

C. 4

D. 8

The molar mass of an ideal gas is $M$. A fixed mass $m$ of the gas expands at a constant pressure $p$. The graph shows the variation with temperature T of the gas volume V.

What is the gradient of the graph?

A.  $\frac{Mp}{mR}$

B.  $\frac{MR}{mp}$

C.  $\frac{mp}{MR}$

D.  $\frac{mR}{Mp}$

A container holds 20 g of argon-40(${}_{18}^{40}\text{Ar}$)  and 40 g of neon-20 (${}_{10}^{20}\text{Ne}$) .

What is$\frac{\text{number of atoms of argon -40}}{\text{number of atoms of neon -20}}$ in the container?

A. 0.25

B. 0.5

C. 2

D. 4

The molar mass of helium is 4.0 g mol^-1. Show that the mass of a helium atom is 6.6 × 10^-27 kg.

Show that the number of helium atoms in the container is about 4 × 10²⁰.

Calculate the ratio  $\frac{\text{total volume of helium atoms}}{\text{volume of helium gas}}$.

Explain, using your answer to (d)(i) and with reference to the kinetic model, why this sample of helium can be assumed to be an ideal gas.

The molar mass of helium is 4.0 g mol^-1. Show that the mass of a helium atom is 6.6 × 10^-27 kg.

Show that the number of helium atoms in the container is about 4 × 10²⁰.

Calculate the ratio  $\frac{\text{total volume of helium atoms}}{\text{volume of helium gas}}$.

Explain, using your answer to (d)(i) and with reference to the kinetic model, why this sample of helium can be assumed to be an ideal gas.

Show that the number of helium atoms in the container is 4 × 10²⁰.

Calculate the ratio $\frac{\text{volume of helium atoms}}{\text{volume of helium gas}}$.

Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.

Show that the number of helium atoms in the container is 4 × 10²⁰.

Calculate the ratio $\frac{\text{volume of helium atoms}}{\text{volume of helium gas}}$.

Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.

The molar mass of water is 18 g mol⁻¹. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

The molar mass of water is 18 g mol⁻¹. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

A fixed mass of an ideal gas has a volume of $V$, a pressure of p and a temperature of $30 °\text{C}$. The gas is compressed to the volume of $\frac{V}{6}$ and its pressure increases to 12p. What is the new temperature of the gas?

A.  $15 °\text{C}$

B.  $60 °\text{C}$

C.  $333 °\text{C}$

D.  $606 °\text{C}$

The equation $\frac{pV}{T}$ = constant is applied to a real gas where p is the pressure of the gas, V is its volume and T is its temperature.

What is correct about this equation?

A. It is empirical.

B. It is theoretical.

C. It cannot be tested.

D. It cannot be disproved.

A gas storage tank of fixed volume V contains N molecules of an ideal gas at temperature T. The pressure at kelvin temperature T is 20 MPa. $\frac{N}{4}$ molecules are removed and the temperature changed to 2T. What is the new pressure of the gas?

A. 10 MPa

B. 15 MPa

C. 30 MPa

D. 40 MPa

Two containers X and Y are maintained at the same temperature. X has volume $4 {\mathrm{m}}^3$ and Y has volume $6 {\mathrm{m}}^3$. They both hold an ideal gas. The pressure in X is $100 \mathrm{Pa}$ and the pressure in Y is $50 \mathrm{Pa}$. The containers are then joined by a tube of negligible volume. What is the final pressure in the containers?

A.  $70 \mathrm{Pa}$

B.  $75 \mathrm{Pa}$

C.  $80 \mathrm{Pa}$

D.  $150 \mathrm{Pa}$

Two identical containers X and Y each contain an ideal gas. X has N molecules of gas at an absolute temperature of T and Y has 3N molecules of gas at an absolute temperature of $\frac{T}{2}$ What is the ratio of the pressures $\frac{P_Y}{P_X}$?

A.   $\frac{1}{6}$

B.   $\frac{2}{3}$

C.   $\frac{3}{2}$

D.   $6$

A substance in the gas state has a density about $1000$ times less than when it is in the liquid state. The diameter of a molecule is $d$. What is the best estimate of the average distance between molecules in the gas state?

A.  $d$

B.  $10d$

C.  $100d$

D.  $1000d$

A sample of oxygen gas with a volume of $3.0 {\text{m}}^3$ is at $100 °\text{C}$. The gas is heated so that it expands at a constant pressure to a final volume of $6.0 {\text{m}}^3$. What is the final temperature of the gas?

A. $750 °\text{C}$

B. $470 °\text{C}$

C. $370 °\text{C}$

D. $200 °\text{C}$

Three statements about Boltzmann’s constant k_B are:

I.   k_B has a unit of J K⁻¹

II.  k_B $=\frac{\text{gas constant}}{\text{Avogadro's constant}}$

III. k_B $=\frac{\text{the average kinetic energy of particles}}{\text{temperature of the gas}}$

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

The water is heated. Explain why the quantity of air in the storage tank decreases.

The water is heated. Explain why the quantity of air in the storage tank decreases.

Gases in the atmosphere are compounds of ${}_6{}^{12}\text{C}$, ${}_1{}^1\text{H}$, ${}_8{}^{16}\text{O}$ and ${}_7{}^{14}\text{N}$.

Four of these gases are CO₂, N₂O, CH₄ and H₂O. A pure sample of each gas is produced. Each sample has the same mass.

Which sample contains the greatest number of molecules?

A.  N₂O

B.  H₂O

C.  CO₂

D.  CH₄

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

A sample of a gas has volume $V$ and contains $N$ molecules, each of mass $m$. The average translational speed of the molecules is $u$.

Which expression is equivalent to the pressure of the gas?

A.  $\frac{1}{3}\frac{NV}{m}{u}^2$

B.  $\frac{1}{3}\frac{Nm}{V}{u}^2$

C.  $\frac{1}{3}\frac{N}{mV}{u}^2$

D.  $\frac{1}{3}\frac{m}{NV}{u}^2$

Calculate the maximum temperature of the gas during the cycle.

Calculate the maximum temperature of the gas during the cycle.

Determine, using the graph, whether the gas acts as an ideal gas.

Calculate, in g, the mass of the gas.

Determine, using the graph, whether the gas acts as an ideal gas.

Calculate, in g, the mass of the gas.

Determine, using the graph, whether the gas acts as an ideal gas.

Calculate, in g, the mass of the gas.

Determine, using the graph, whether the gas acts as an ideal gas.

Calculate, in g, the mass of the gas.

A vessel contains a mass X of helium gas and a mass 2X of oxygen gas.

Molar mass of helium = 4 g

Molar mass of oxygen = 32 g

What is the $\frac{\mathrm{number} \mathrm{of} \mathrm{helium} \mathrm{atoms}}{\mathrm{number} \mathrm{of} \mathrm{oxygen} \mathrm{molecules}}$?

A.  $\frac{1}{8}$

B.  $\frac{1}{4}$

C.  4

D.  8

Discuss how the motion of the molecules of a gas gives rise to pressure in the gas.

The average speed of the molecules of a gas is 500 m s⁻¹. The density of the gas is 1.2 kg m⁻³. Calculate, in kPa, the pressure of the gas.

Discuss how the motion of the molecules of a gas gives rise to pressure in the gas.

The average speed of the molecules of a gas is 500 m s⁻¹. The density of the gas is 1.2 kg m⁻³. Calculate, in kPa, the pressure of the gas.

Calculate the average translational speed of air molecules.

The air is a mixture of nitrogen, oxygen and other gases. Explain why the component gases of air in the container have different average translational speeds.

The temperature of the sample is increased without a change in pressure. Outline the effect it has on the density of the gas.

Calculate the average translational speed of air molecules.

The air is a mixture of nitrogen, oxygen and other gases. Explain why the component gases of air in the container have different average translational speeds.

The temperature of the sample is increased without a change in pressure. Outline the effect it has on the density of the gas.

the ideal gas law,

the kinetic energy of particles in an ideal gas.

A container holds a mixture of argon and helium atoms at a temperature of 37 °C.

Calculate the average translational speed of the argon atoms.

The molar mass of argon is 4.0 × 10⁻² kg mol⁻¹.

the ideal gas law,

the kinetic energy of particles in an ideal gas.

A container holds a mixture of argon and helium atoms at a temperature of 37 °C.

Calculate the average translational speed of the argon atoms.

The molar mass of argon is 4.0 × 10⁻² kg mol⁻¹.

Calculate the pressure of the gas in the container.

Determine the mass of the gas in the container.

Calculate the average translational speed of the gas particles.

The temperature of the gas in the container is increased.

Explain, using the kinetic theory, how this change leads to a change in pressure in the container.

Calculate the pressure of the gas in the container.

Determine the mass of the gas in the container.

Calculate the average translational speed of the gas particles.

The temperature of the gas in the container is increased.

Explain, using the kinetic theory, how this change leads to a change in pressure in the container.

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

Show that during an adiabatic expansion of an ideal monatomic gas the temperature $T$ and volume $V$ are given by

$T{V}^{\frac{2}{3}}$ = constant