Topic 8: Energy production

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.  $\frac{I}{3125}$

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.  $\frac{I}{3125}$

The power station has a useful power output of $1.2 \mathrm{GW}$ and an efficiency of $36 \%$. Determine the mass of U-235 that undergoes fission in one day.

The power station has a useful power output of $1.2 \mathrm{GW}$ and an efficiency of $36 \%$. Determine the mass of U-235 that undergoes fission in one day.

The power station has a useful power output of $1.2 \mathrm{GW}$ and an efficiency of $36 \%$. Determine the mass of U-235 that undergoes fission in one day.

Estimate, in $\mathrm{J} {\mathrm{kg}}^{-1}$, the specific energy of U-235.

Estimate, in $\mathrm{J} {\mathrm{kg}}^{-1}$, the specific energy of U-235.

Estimate, in $\mathrm{J} {\mathrm{kg}}^{-1}$, the specific energy of U-235.

Estimate, in $\mathrm{J} {\mathrm{kg}}^{-1}$, the specific energy of U-235.

Estimate, in $\mathrm{J} {\mathrm{kg}}^{-1}$, the specific energy of U-235.

Estimate, in $\mathrm{J} {\mathrm{kg}}^{-1}$, the specific energy of U-235.

The energy density of a substance can be calculated by multiplying its specific energy with which quantity?

A. mass

B. volume

C. $\frac{\text{mass}}{\text{volume}}$

D. $\frac{\text{volume}}{\text{mass}}$

The energy density of a substance can be calculated by multiplying its specific energy with which quantity?

A. mass

B. volume

C. $\frac{\text{mass}}{\text{volume}}$

D. $\frac{\text{volume}}{\text{mass}}$

A black body emits radiation with its greatest intensity at a wavelength of I_max. The surface temperature of the black body doubles without any other change occurring. What is the wavelength at which the greatest intensity of radiation is emitted?

A. I_max

B. $\frac{\text{I}{}_{\text{max}}}{\text{2}}$

C. $\frac{\text{I}{}_{\text{max}}}{\text{4}}$

D. $\frac{\text{I}{}_{\text{max}}}{\text{16}}$

A black body emits radiation with its greatest intensity at a wavelength of I_max. The surface temperature of the black body doubles without any other change occurring. What is the wavelength at which the greatest intensity of radiation is emitted?

A. I_max

B. $\frac{\text{I}{}_{\text{max}}}{\text{2}}$

C. $\frac{\text{I}{}_{\text{max}}}{\text{4}}$

D. $\frac{\text{I}{}_{\text{max}}}{\text{16}}$

Determine the mean temperature of the Earth.

Determine the mean temperature of the Earth.

Determine the mean temperature of the Earth.

The albedo of the planet is ${\alpha }_{\text{p}}$. The equilibrium surface temperature of the planet is T. Derive the expression

$T=\sqrt[4]{\frac{P(1-{\alpha }_{\text{p}})}{16\pi d^{2}e\sigma }}$

where e is the emissivity of the planet.

The albedo of the planet is ${\alpha }_{\text{p}}$. The equilibrium surface temperature of the planet is T. Derive the expression

$T=\sqrt[4]{\frac{P(1-{\alpha }_{\text{p}})}{16\pi d^{2}e\sigma }}$

where e is the emissivity of the planet.

The albedo of the planet is ${\alpha }_{\text{p}}$. The equilibrium surface temperature of the planet is T. Derive the expression

$T=\sqrt[4]{\frac{P(1-{\alpha }_{\text{p}})}{16\pi d^{2}e\sigma }}$

where e is the emissivity of the planet.

Explain why the power incident on the planet is

                                                                $\frac{P}{4\pi d^2}\times \frac{A}{4}.$

Explain why the power incident on the planet is

                                                                $\frac{P}{4\pi d^2}\times \frac{A}{4}.$

Explain why the power incident on the planet is

                                                                $\frac{P}{4\pi d^2}\times \frac{A}{4}.$

The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m⁻².

A measure of the efficiency of a photovoltaic cell is the ratio

$\frac{\text{energy available every second to the external circuit}}{\text{energy arriving every second at the photovoltaic cell surface}}.$

Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.

The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m⁻².

A measure of the efficiency of a photovoltaic cell is the ratio

$\frac{\text{energy available every second to the external circuit}}{\text{energy arriving every second at the photovoltaic cell surface}}.$

Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.

The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m⁻².

A measure of the efficiency of a photovoltaic cell is the ratio

$\frac{\text{energy available every second to the external circuit}}{\text{energy arriving every second at the photovoltaic cell surface}}.$

Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.

A model of an ideal wind turbine with blade length $l_0$ is designed to produce a power $P$ when the average wind speed is $v$. A second ideal wind turbine is designed to produce a power $\frac{P}{2}$ when the average wind speed is $\frac{v}{2}$. What is the blade length for the second wind turbine?

A.  $\frac{l_0}{2}$

B.  $l_0$

C.  $2 l_0$ 

D.  $4 l_0$

A model of an ideal wind turbine with blade length $l_0$ is designed to produce a power $P$ when the average wind speed is $v$. A second ideal wind turbine is designed to produce a power $\frac{P}{2}$ when the average wind speed is $\frac{v}{2}$. What is the blade length for the second wind turbine?

A.  $\frac{l_0}{2}$

B.  $l_0$

C.  $2 l_0$ 

D.  $4 l_0$

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

What is equivalent to $\frac{\text{specific energy of a fuel}}{\text{energy density of a fuel}}$?

A.     density of the fuel

B.     $\frac{1}{\text{density of the fuel}}$

C.     $\frac{\text{energy stored in the fuel}}{\text{density of the fuel}}$

D.     $\frac{\text{density of the fuel}}{\text{energy stored in the fuel}}$

What is equivalent to $\frac{\text{specific energy of a fuel}}{\text{energy density of a fuel}}$?

A.     density of the fuel

B.     $\frac{1}{\text{density of the fuel}}$

C.     $\frac{\text{energy stored in the fuel}}{\text{density of the fuel}}$

D.     $\frac{\text{density of the fuel}}{\text{energy stored in the fuel}}$

State what is meant by thermal radiation.

State what is meant by thermal radiation.

State what is meant by thermal radiation.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Derive the units of intensity in terms of fundamental SI units.

Derive the units of intensity in terms of fundamental SI units.

Derive the units of intensity in terms of fundamental SI units.

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

A wind turbine has a power output p when the wind speed is v. The efficiency of the wind turbine does not change. What is the wind speed at which the power output is $\frac{p}{2}$?

A.     $\frac{v}{4}$

B.     $\frac{v}{\sqrt{8}}$

C.     $\frac{v}{2}$

D.     $\frac{v}{\sqrt[3]{2}}$

A wind turbine has a power output p when the wind speed is v. The efficiency of the wind turbine does not change. What is the wind speed at which the power output is $\frac{p}{2}$?

A.     $\frac{v}{4}$

B.     $\frac{v}{\sqrt{8}}$

C.     $\frac{v}{2}$

D.     $\frac{v}{\sqrt[3]{2}}$

Three gases in the atmosphere are

          I.     carbon dioxide (CO₂)

          II.     dinitrogen monoxide (N₂O)

          III.     oxygen (O₂).

Which of these are considered to be greenhouse gases?

A.     I and II only

B.     I and III only

C.     II and III only

D.     I, II and III

Three gases in the atmosphere are

          I.     carbon dioxide (CO₂)

          II.     dinitrogen monoxide (N₂O)

          III.     oxygen (O₂).

Which of these are considered to be greenhouse gases?

A.     I and II only

B.     I and III only

C.     II and III only

D.     I, II and III

Mars and Earth act as black bodies. The $\frac{\text{power radiated by Mars}}{\text{power radiated by the Earth}}=p$ and $\frac{\text{absolute mean temperature of the surface of Mars}}{\text{absolute mean temperature of the surface of the Earth}}=t$.

What is the value of $\frac{\text{radius of Mars}}{\text{radius of the Earth}}$?

A.     $\frac{p}{t^4}$

B.     $\frac{\sqrt{p}}{t^2}$

C.     $\frac{t^4}{p}$

D.     $\frac{t^2}{\sqrt{p}}$

Mars and Earth act as black bodies. The $\frac{\text{power radiated by Mars}}{\text{power radiated by the Earth}}=p$ and $\frac{\text{absolute mean temperature of the surface of Mars}}{\text{absolute mean temperature of the surface of the Earth}}=t$.

What is the value of $\frac{\text{radius of Mars}}{\text{radius of the Earth}}$?

A.     $\frac{p}{t^4}$

B.     $\frac{\sqrt{p}}{t^2}$

C.     $\frac{t^4}{p}$

D.     $\frac{t^2}{\sqrt{p}}$

After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.

After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.

After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.

Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.

Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.

Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.

Show that the average rate at which the gravitational potential energy of the water decreases is 2.5 GW.

Show that the average rate at which the gravitational potential energy of the water decreases is 2.5 GW.

Show that the average rate at which the gravitational potential energy of the water decreases is 2.5 GW.

The storage system produces 1.8 GW of electrical power. Determine the overall efficiency of the storage system.

The storage system produces 1.8 GW of electrical power. Determine the overall efficiency of the storage system.

The storage system produces 1.8 GW of electrical power. Determine the overall efficiency of the storage system.

A fuel has mass density $\rho$ and energy density $u$. What mass of the fuel has to be burned to release thermal energy $E$?

A.  $\frac{\rho E}{u}$

B.  $\frac{uE}{\rho }$

C.  $\frac{\rho u}{E}$

D.  $\rho uE$

A fuel has mass density $\rho$ and energy density $u$. What mass of the fuel has to be burned to release thermal energy $E$?

A.  $\frac{\rho E}{u}$

B.  $\frac{uE}{\rho }$

C.  $\frac{\rho u}{E}$

D.  $\rho uE$

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

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

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

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.

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.

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.

A photovoltaic panel of area S has an efficiency of 20 %. A second photovoltaic panel has an efficiency of 15 %. What is the area of the second panel so that both panels produce the same power under the same conditions?

A.   $\frac{S}{3}$

B.   $\frac{3S}{4}$

C.   $\frac{5S}{4}$

D.   $\frac{4S}{3}$

A photovoltaic panel of area S has an efficiency of 20 %. A second photovoltaic panel has an efficiency of 15 %. What is the area of the second panel so that both panels produce the same power under the same conditions?

A.   $\frac{S}{3}$

B.   $\frac{3S}{4}$

C.   $\frac{5S}{4}$

D.   $\frac{4S}{3}$

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Wind of speed $v$ flows through a wind generator. The wind speed drops to $\frac{v}{3}$ after passing through the blades. What is the maximum possible efficiency of the generator?

A.  $\frac{1}{27}$

B.  $\frac{8}{27}$

C.  $\frac{19}{27}$

D.  $\frac{26}{27}$

Wind of speed $v$ flows through a wind generator. The wind speed drops to $\frac{v}{3}$ after passing through the blades. What is the maximum possible efficiency of the generator?

A.  $\frac{1}{27}$

B.  $\frac{8}{27}$

C.  $\frac{19}{27}$

D.  $\frac{26}{27}$

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.  $1$

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.  $1$

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 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.

Some fuel sources are renewable. Outline what is meant by renewable.

Some fuel sources are renewable. Outline what is meant by renewable.

Some fuel sources are renewable. Outline what is meant by renewable.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Some fuel sources are renewable. Outline what is meant by renewable.

Some fuel sources are renewable. Outline what is meant by renewable.

Some fuel sources are renewable. Outline what is meant by renewable.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

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 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 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.

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.

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.

Suggest why the answer in (a) is a maximum.

Suggest why the answer in (a) is a maximum.

Suggest why the answer in (a) is a maximum.

Determine the maximum power that can be extracted from the wind by this turbine.

Determine the maximum power that can be extracted from the wind by this turbine.

Determine the maximum power that can be extracted from the wind by this turbine.

A fusion reaction of one nucleus of hydrogen-2 and one nucleus of hydrogen-3 converts 0.019 u to energy. A fission reaction of one nucleus of uranium-235 converts a mass of 0.190 u to energy.

What is the ratio $\frac{\text{specific energy of this fusion of hydrogen}}{\text{specific energy of this fission of uranium}}$?

A.  0.1

B.  0.2

C.  5

D.  10

A fusion reaction of one nucleus of hydrogen-2 and one nucleus of hydrogen-3 converts 0.019 u to energy. A fission reaction of one nucleus of uranium-235 converts a mass of 0.190 u to energy.

What is the ratio $\frac{\text{specific energy of this fusion of hydrogen}}{\text{specific energy of this fission of uranium}}$?

A.  0.1

B.  0.2

C.  5

D.  10

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?

Water is to be pumped through a vertical height difference of 12.5 m. The pump is driven by a wind turbine that has an efficiency of 50 % and an area swept by the blades of 100 m². The average wind speed is 5.0 m s⁻¹ and the air density is 1.2 kg m⁻³.

What is the maximum mass of water that can be pumped every second?

A.  3 kg

B.  30 kg

C.  60 kg

D.  120 kg

Water is to be pumped through a vertical height difference of 12.5 m. The pump is driven by a wind turbine that has an efficiency of 50 % and an area swept by the blades of 100 m². The average wind speed is 5.0 m s⁻¹ and the air density is 1.2 kg m⁻³.

What is the maximum mass of water that can be pumped every second?

A.  3 kg

B.  30 kg

C.  60 kg

D.  120 kg

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.

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

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

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

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.

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

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

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

State what is meant by thermal radiation.

State what is meant by thermal radiation.

State what is meant by thermal radiation.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

The power station has a useful power output of $1.2 \mathrm{GW}$ and an efficiency of $36 \%$. Determine the mass of U-235 that undergoes fission in one day.

The power station has a useful power output of $1.2 \mathrm{GW}$ and an efficiency of $36 \%$. Determine the mass of U-235 that undergoes fission in one day.

The power station has a useful power output of $1.2 \mathrm{GW}$ and an efficiency of $36 \%$. Determine the mass of U-235 that undergoes fission in one day.

The specific energy of fossil fuel is typically $30 \text{MJ} {\text{kg}}^{–1}$. Suggest, with reference to your answer to (b)(i), one advantage of U-235 compared with fossil fuels in a power station.

The specific energy of fossil fuel is typically $30 \text{MJ} {\text{kg}}^{–1}$. Suggest, with reference to your answer to (b)(i), one advantage of U-235 compared with fossil fuels in a power station.

The specific energy of fossil fuel is typically $30 \text{MJ} {\text{kg}}^{–1}$. Suggest, with reference to your answer to (b)(i), one advantage of U-235 compared with fossil fuels in a power station.

On average, the Moon is the same distance from the Sun as the Earth. The Moon can be assumed to have an emissivity e = 1 and an albedo ${\alpha }_{\text{M}}$ = 0.13. The solar constant is 1.36 × 103 W m⁻². Calculate the surface temperature of the Moon.

On average, the Moon is the same distance from the Sun as the Earth. The Moon can be assumed to have an emissivity e = 1 and an albedo ${\alpha }_{\text{M}}$ = 0.13. The solar constant is 1.36 × 103 W m⁻². Calculate the surface temperature of the Moon.

On average, the Moon is the same distance from the Sun as the Earth. The Moon can be assumed to have an emissivity e = 1 and an albedo ${\alpha }_{\text{M}}$ = 0.13. The solar constant is 1.36 × 103 W m⁻². Calculate the surface temperature of the Moon.

State two reasons why future energy demands will be increasingly reliant on sources such as photovoltaic cells.

State two reasons why future energy demands will be increasingly reliant on sources such as photovoltaic cells.

State two reasons why future energy demands will be increasingly reliant on sources such as photovoltaic cells.

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 $\frac{{\lambda }_{\text{ρ}}}{2}$?

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 $\frac{{\lambda }_{\text{ρ}}}{2}$?

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.  $16P_0$

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.

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.  $\frac{16}{9}$

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)

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.  $2\mathrm{\Delta }T$

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.

An ac generator produces a root mean square (rms) voltage V. What is the peak output voltage when the frequency is doubled?

A.  $\frac{2}{\sqrt{2}}V$

B.  $\frac{V}{2\sqrt{2}}$

C.  $\frac{\sqrt{2}}{2}V$

D.  $2\sqrt{2}V$

An ac generator produces a root mean square (rms) voltage V. What is the peak output voltage when the frequency is doubled?

A.  $\frac{2}{\sqrt{2}}V$

B.  $\frac{V}{2\sqrt{2}}$

C.  $\frac{\sqrt{2}}{2}V$

D.  $2\sqrt{2}V$

Two capacitors C₁ and C₂ are connected in series to a cell as shown. The capacitance of C₁ is four times the capacitance of C₂. The charge stored on C₁ is q₁ and the charge stored on C₂ is q₂.

What is $\frac{q_1}{q_2}$?

A.  $\frac{1}{4}$

B.  $\frac{4}{5}$

C.  1

D.  4

Two capacitors C₁ and C₂ are connected in series to a cell as shown. The capacitance of C₁ is four times the capacitance of C₂. The charge stored on C₁ is q₁ and the charge stored on C₂ is q₂.

What is $\frac{q_1}{q_2}$?

A.  $\frac{1}{4}$

B.  $\frac{4}{5}$

C.  1

D.  4

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².