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

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

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 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 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 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.     $\frac{v}{\sqrt[3]{2}}$

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

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

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.  $\rho uE$

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

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.

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

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

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.

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.

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.

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.

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

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 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.

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

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 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.  $4 l_0$

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.

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.

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

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.  $\frac{26}{27}$