91Ó°ÊÓ

A brass rod is in thermal contact with a constant-temperature reservoir at \(130^{\circ} \mathrm{C}\) at one end and a constant-temperature reservoir at \(24.0^{\circ} \mathrm{C}\) at the other end. (a) Compute the total change in entropy of the rod-reservoirs system when \(5030 \mathrm{~J}\) of energy is conducted through the rod, from one reservoir to the other. (b) Does the entropy of the rod change?

Calculate the efficiency of a fossil-fuel power plant that consumes 380 metric tons of coal each hour to produce useful work at the rate of \(750 \mathrm{MW}\). The heat of combustion of coal (the heat due to burning it) is \(28 \mathrm{MJ} / \mathrm{kg}\).

A Carnot refrigerator extracts \(35.0 \mathrm{~kJ}\) as heat during each cycle, operating with a coefficient of performance of \(4.60 .\) What are (a) the energy per cycle transferred as heat to the room and (b) the work done per cycle?

A Carnot engine whose high-temperature reservoir is at \(400 \mathrm{~K}\) has an efficiency of \(30.0 \% .\) By how much should the temperature of the low- temperature reservoir be changed to increase the efficiency to \(40.0 \% ?\)

Find the relation between the efficiency of a reversible ideal heat engine and the coefficient of performance of the reversible refrigerator obtained by running the engine backwards.

A Carnot engine has a power of \(500 \mathrm{~W}\). It operates between heat reservoirs at \(100^{\circ} \mathrm{C}\) and \(60.0^{\circ} \mathrm{C}\). Calculate (a) the rate of heat input and (b) the rate of exhaust heat output.

In a real refrigerator, the low-temperature coils are at \(-13^{\circ} \mathrm{C}\), and the compressed gas in the condenser is at \(26^{\circ} \mathrm{C}\). What is the theoretical coefficient of performance?