Winter heating of an office building requires an average of $250 \mathrm{kBtu} / \mathrm{h}$. The heating system uses a heat pump with $\mathrm{COP}=$ 3.0. (a) If the energy supplied to the heat pump costs $\$ 0.09 / \mathrm{kWh}$, what's the cost per day to heat the building?

A refrigerator with $\mathrm{COP}=3.8$ consumes electrical energy at the rate of 600 W. At what rate can this refrigerator remove heat from its interior?

A power plant produces electrical energy at the rate of 1300 MW with an efficiency of $0.31$. The excess heat is dumped into a river that carries $1500 \mathrm{~m}^3 / \mathrm{s}$ of water. How much does the river's temperature increase?

One alternative energy source is the temperature difference between surface and deep water in the tropical oceans. Suppose a heat engine uses $25^{\circ} \mathrm{C}$ surface water as its hot reservoir and $4^{\circ} \mathrm{C}$ deep water as its cold reservoir. (b) How much heat would have to be removed from the surface water each day in order to produce energy at the rate of a typical large power plant, about $1000 \mathrm{MW}$ ?

One alternative energy source is the temperature difference between surface and deep water in the tropical oceans. Suppose a heat engine uses $25^{\circ} \mathrm{C}$ surface water as its hot reservoir and $4^{\circ} \mathrm{C}$ deep water as its cold reservoir. (a) Find the maximum efficiency of such an engine.

Find the maximum temperature in a Camot cycle operating in a room-temperature $\left(20^{\circ} \mathrm{C}\right)$ environment if its Carnot efficiency is $0.5$.

Find the maximum possible efficiency of a heat engine operating between the freezing and boiling points of water.

An automobile engine with an efficiency $0.21$ dumps heat to the environment at the rate of $330 \mathrm{~kW}$. What's its mechanical power output, in W and in hp?

Each second a nuclear power plant extracts $1700 \mathrm{MJ}$ of thermal energy from its uranium fuel and dumps $1100 \mathrm{MJ}$ of waste heat into a river. (b) At what rate does it produce electrical energy, assuming all the work it does ends up as electricity?

Each second a nuclear power plant extracts $1700 \mathrm{MJ}$ of thermal energy from its uranium fuel and dumps $1100 \mathrm{MJ}$ of waste heat into a river. (a) What's its efficiency?

A $40 \%$ efficient heat engine does mechanical work at the rate of $400 \mathrm{~W}$. If it runs for an entire day, find the heat removed from the hot reservoir and the heat transferred to the cold reservoir.

A heat engine does $650 \mathrm{~J}$ of work and dumps $1270 \mathrm{~J}$ of heat to its cold reservoir. What's its efficiency?

Earth receives energy from the Sun at an average rate of about $240 \mathrm{~W} / \mathrm{m}^2$. Given Earth's average temperature of $15^{\circ} \mathrm{C}$, find the rate of entropy increase associated with this energy flow.

Find the entropy increase when $100 \mathrm{~g}$ of nitrogen boil at atmospheric pressure.