DP Physics Questionbank

X and Y are two spherical black-body radiators that emit the same total power. The absolute temperature of X is half that of Y. 

What is $\frac{\text{radius of X}}{\text{radius of Y}}$?

A. 4

B. 8 

C. 16 

D. 32

Explain, using your answer to (b), why countries are being asked to decrease their dependence on fossil fuels.

The average surface temperature of Mars is approximately 200 K and the average surface temperature of Earth is approximately 300 K. Mars has a radius half that of Earth. Assume that both Mars and Earth act as black bodies.

What is $\frac{\text{power radiated by Mars}}{\text{power radiated by Earth}}$?

A.  20
B.  5
C.  0.2
D.  0.05

A room is at a constant temperature of 300 K. A hotplate in the room is at a temperature of 400 K and loses energy by radiation at a rate of P. What is the rate of loss of energy from the hotplate when its temperature is 500 K?

A.  $\frac{4^4}{5^4}$P

B.  $\frac{5^4+3^4}{4^4+3^4}$P

C.  $\frac{5^4}{4^4}$P

D.  $\frac{5^4-3^4}{4^4-3^4}$P

The hydroelectric system has four 250 MW generators. The specific energy available from the water is 2.7 kJ kg^–1. Determine the maximum time for which the hydroelectric system can maintain full output when a mass of 1.5 x 10¹⁰ kg of water passes through the turbines.

At the location of the hydroelectric system, an average intensity of 180 W m^–2 arrives at the Earth’s surface from the Sun. Solar photovoltaic (PV) cells convert this solar energy with an efficiency of 22 %. The solar cells are to be arranged in a square array. Determine the length of one side of the array that would be required to replace the
hydroelectric system.

The average albedo of glacier ice is 0.25.

What is $\frac{\text{power absorbed by glacier ice}}{\text{power reflected by glacier ice}}$?

A.  0.25

B.  0.33

C.  2.5

D.  3.0

A solar farm is made up of photovoltaic cells of area 25 000 m². The average solar intensity falling on the farm is 240 W m^–2 and the average power output of the farm is 1.6 MW. Calculate the efficiency of the photovoltaic cells.

The hydroelectric system has four 250 MW generators. Determine the maximum time for which the hydroelectric system can maintain full output when a mass of 1.5 x 10¹⁰ kg of water passes through the turbines.

Explain two reasons why the number of turbines required is likely to be greater than your answer to (c)(i).

Determine the minimum number of turbines needed to generate the same power as the solar farm.

The water in a particular pumped storage hydroelectric system falls a vertical distance of 270 m to the turbines. Calculate the speed at which water arrives at the turbines. Assume that there is no energy loss in the system.

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.

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

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.

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

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.

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

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

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.

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.

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 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 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.

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

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.

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.

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

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

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.

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.

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.  $\rho uE$

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.

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.

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

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.

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

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.

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 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.

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

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.

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.

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.

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

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