The intensity of solar radiations incident on a planet is $\mathrm{S}$ . The diagram represents the energy balance of the planet. The atmosphere reflects an intensity $0.20 \mathrm{S}$and radiates$0.35 \mathrm{S}$. The surface reflects $0.05 \mathrm{S}$ and radiates $0.40 \mathrm{S}$. What is the albedo of the planet.

A nuclear power plant produces $800 \mathrm{MW}$ of electricity with an overall efficiency of$0.32$. The fission reaction taking place in the core of the reactor is:

${}_0{}^1\mathrm{n}+{}_{92}{}^{235}\mathrm{U}\to {}_{54}{}^{140}\mathrm{Xe}+{}_{38}{}^{94}\mathrm{Sr}+2{}_0{}^1\mathrm{n}$ 

 (i) Using the masses provided below show that the energy released in one fission is about $180 \mathrm{MeV}$

${}_0{}^1\mathrm{n}=1.009 \mathrm{u} , {}_{92}{}^{235}\mathrm{U}=235.044 ,{}_{54}{}^{140}\mathrm{Xe}=139.992, {}_{38}{}^{94}\mathrm{Sr}=93.915$

(ii) Estimate the specific energy of $U-235$

(iii)Show that the mass of uranium undergoing fission in one year is about $1500 \mathrm{kg}$

In a nuclear reactor. describe the role of, 

(i) The moderator

(ii) The control rods

(iii) The heat exchanger

In a pumped storage system, the high reservoir of water has area$4.8\times {10}^4{\mathrm{m}}^2$and an average depth of $38 \mathrm{m}$. When the water from the reservoir falls to a lower reservoir, the centre of the mass of the water is lowered by a vertical difference of $225 \mathrm{m}$. The water flows through a turbine connected to a generator at a rate of $350 {\mathrm{m}}^3{\mathrm{s}}^{-1}$.

 Determine the loss of gravitational potential energy when the upper reservoir has been completely emptied.

In a pumped storage system, the high reservoir of water has area$4.8\times {10}^4{\mathrm{m}}^2$and an average depth of $38 \mathrm{m}$. When the water from the reservoir falls to a lower reservoir, the centre of the mass of the water is lowered by a vertical difference of $225 \mathrm{m}$. The water flows through a turbine connected to a generator at a rate of $350 {\mathrm{m}}^3{\mathrm{s}}^{-1}$.

 Estimate the power supply by the falling water.

In a pumped storage system, the high reservoir of water has area$4.8\times {10}^4{\mathrm{m}}^2$and an average depth of $38 \mathrm{m}$. When the water from the reservoir falls to a lower reservoir, the centre of the mass of the water is lowered by a vertical difference of $225 \mathrm{m}$. The water flows through a turbine connected to a generator at a rate of $350 {\mathrm{m}}^3{\mathrm{s}}^{-1}$.

The efficiency of the plant for converting the energy into electricity is $0.60$. The price of electricity sold by this power plant at peak time is $\$0.12\mathrm{per} \mathrm{kWh}$. The plant can by off-peak electrical power at $\$0.07 \mathrm{per} \mathrm{kWh}$. The efficiency at which the water can be pumped back to the high reservoir is $0.64$.

 Estimate the profit made by the power plant for single emptying and filling of the high reservoir