Chapter 15: The Laws of Thermodynamics

Question:(I) A heat engine’s high temperature\({T_{\bf{H}}}\)could be ambient temperature, because liquid nitrogen at 77 K could be\({T_{\bf{L}}}\)and is cheap. What would be the efficiency of a Carnot engine that made use of heat transferred from air at room temperature (293 K) to the liquid nitrogen “fuel”(Fig.15–25)?

Question:(II) Which will improve the efficiency of a Carnot engine more: a 10 °C increase in the high-temperature reservoir, or a 10 °C decrease in the low temperature reservoir? Give detailed results. Can you state a generalization?

Question:(II) A certain power plant puts out 580 MW of electric power. Estimate the heat discharged per second, assuming that the plant has an efficiency of 32%.

Question:(II) A nuclear power plant operates at 65% of its maximum theoretical (Carnot) efficiency between temperatures of 660°C and 330°C. If the plant produces electric energy at the rate of 1.4 GW, how much exhaust heat is discharged per hour?

Question:(II) A heat engine exhausts its heat at 340°C and has a Carnot efficiency of 36%. What exhaust temperature would enable it to achieve a Carnot efficiency of 42%?

Question:(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 (a) the work done per second, and (b) the total heat input per second from the gasoline. (c) If the energy content of gasoline is 130 MJ per gallon, how long does one gallon last?

Question:(II) A Carnot engine performs work at the rate of 520 kW with an input of 950 kcal of heat per second. If the temperature of the heat source is 520°C, at what temperature is the waste heat exhausted?

(I) One liter of air is cooled at constant pressure until its volume is halved, and then it is allowed to expand isothermally back to its original volume. Draw the process on a PV diagram.

Question:(II) A heat engine uses a heat source at 580°C and has an ideal (Carnot) efficiency of 22%. To increase the ideal efficiency to 42%, what must be the temperature of the heat source?

Question:(I) If an ideal refrigerator keeps its contents at 2.5°C when the house temperature is 22°C, what is its COP?