B.1 Thermal energy transfers

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.  $4P$

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.  $4P$

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 $2Q$

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 $2Q$

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 $\propto \frac{1}{{\text{bar diameter}}^2}$

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.

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

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

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

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

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 the specific latent heat of fusion of chocolate.

Estimate the specific latent heat of fusion of chocolate.

Estimate the specific latent heat of fusion of chocolate.

Estimate the specific latent heat of fusion of chocolate.

Estimate the specific latent heat of fusion of chocolate.

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

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

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

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.

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.

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.

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

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.

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.

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.

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.

Calculate the temperature at Y.

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.

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.

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.

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

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 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?

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.  $\frac{16}{9}$

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

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

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.

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.

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.  $\frac{d}{4}$

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.  $\frac{d}{4}$

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.  $\frac{d}{4}$

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.

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.

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.

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.

Calculate the theoretical equilibrium temperature of the mixture.

Calculate the theoretical equilibrium temperature of the mixture.

Calculate the theoretical equilibrium temperature of the mixture.

Calculate the theoretical equilibrium temperature of the mixture.

Calculate the theoretical equilibrium temperature of the mixture.

Calculate the theoretical equilibrium temperature of the mixture.

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

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

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 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. $\frac{gL}{m\mathrm{\Delta }T}$

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

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

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.

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 average speed of the helium atoms in the container.

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

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

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 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 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 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.  $\frac{m{v}^2}{2Mc}$

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

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

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

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

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

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

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

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.  $32 °\text{C}$

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.  $32 °\text{C}$

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.  $16P_0$

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.  $16P_0$

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

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

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

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

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

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

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 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.  $273+\frac{P}{mc}$

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.

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.

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.  $6 m$

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.  $6 m$

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.  $\frac{d}{8}$

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.  $\frac{d}{8}$

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

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

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.

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

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.

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

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.

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

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

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.  $2\mathrm{\Delta }T$

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.  $2\mathrm{\Delta }T$

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.  $2\mathrm{\Delta }T$

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)

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)

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)

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)

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)

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)

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)

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)

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

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

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

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

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

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 the specific latent heat of fusion of chocolate.

Estimate the specific latent heat of fusion of chocolate.

Estimate the specific latent heat of fusion of chocolate.

Estimate the specific latent heat of fusion of chocolate.

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.

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.

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

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

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

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

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

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

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

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

Calculate, in m, the distance to star X.

Calculate, in m, the distance to star X.

Calculate, in m, the distance to star X.

Calculate, in m, the distance to star X.

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

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

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

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