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 $1000 \mathrm{MW}$ ?

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.

Using data from Chapter 13 , find the entropy increase in $1.5 \mathrm{~kg}$ of mercury when it melts at $-39^{\circ} \mathrm{C}$ and 1 atm pressure.

$150 \mathrm{~g}$ of water at $0^{\circ} \mathrm{C}$ are placed in a freezer at $-4^{\circ} \mathrm{C}$. Find the net entropy change after all the water has turned to ice but is still at $0^{\circ} \mathrm{C}$.

Find the net entropy change when a $50-\mathrm{g}$ ice cube initially at $0^{\circ} \mathrm{C}$ melts in (b) a $35^{\circ} \mathrm{C}$ room.

Find the net entropy change when a $50-\mathrm{g}$ ice cube initially at $0^{\circ} \mathrm{C}$ melts in (a) a $10^{\circ} \mathrm{C}$ room.

Find the entropy created when $100 \mathrm{~g}$ of ice melts at $0^{\circ} \mathrm{C}$. Compare with the entropy created when the same mass of water boils at $100^{\circ} \mathrm{C}$.

Find the entropy change when $75 \mathrm{~g}$ of steam condenses to water at $100^{\circ} \mathrm{C}$.