23. The Second Law of Thermodynamics

A Carnot refrigerator is operated between two heat reservoirs at temperatures of $320$ K and $270$ K. What is the coefficient of performance of the refrigerator?

A Carnot refrigerator is operated between two heat reservoirs at temperatures of $320$ K and $270$ K. If the refrigerator completes $165$ cycles each minute, what power input is required to operate it?

A diesel engine performs $2200$ J of mechanical work and discards $4300$ J of heat each cycle. How much heat must be supplied to the engine in each cycle?

A Carnot refrigerator operates between energy reservoirs at 0℃ and 250℃. A 2.4-cm-diameter, 50-cm-long copper bar connects the two energy reservoirs. At what rate, in W, must work be done on the refrigerator to remove heat from the cold reservoir at the same rate that it arrives through the copper bar?

An ideal refrigerator utilizes a Carnot cycle operating between 0℃ and 25℃. To turn 10 kg of liquid water at 0℃ into 10 kg of ice at 0℃, (a) how much heat is exhausted into the room and (b) how much energy must be supplied to the refrigerator?

A Carnot engine operates between temperatures of 5℃ and 500℃. The output is used to run a Carnot refrigerator operating between -5℃ and 25℃. How many joules of heat energy does the refrigerator exhaust into the room for each joule of heat energy used by the heat engine?

FIGURE P21.46 shows a Carnot heat engine driving a Carnot refrigerator. Determine Q₂, Q₃ and Q₄.

A typical coal-fired power plant burns 300 metric tons of coal every hour to generate 750 MW of electricity. 1 metric ton = 1000 kg. The density of coal is 1500 kg/m³ and its heat of combustion is 28 MJ/kg. Assume that all heat is transferred from the fuel to the boiler and that all the work done in spinning the turbine is transformed into electric energy. Suppose the coal is piled up in a 10 m ✕ 10 m room. How tall must the pile be to operate the plant for one day?

A heat engine exhausts 7600 J of heat while performing 2600 J of useful work. What is the efficiency of this engine?

A certain power plant puts out 680 MW of electric power. Estimate the heat discharged per second, assuming that the plant has an efficiency of 32%.

(II) A four-cylinder gasoline engine has an efficiency of 0.22 and delivers 180 J of work per cycle per cylinder. If the engine runs at 25 cycles per second (1500 rpm), determine the work done per second.