A heat engine performs the reversible cycle abca with 9.0 moles of an ideal gas, as shown in the figure. Path ca is an adiabatic process. The temperatures at points a and b are 300 K and 500 K, respectively. The volume at point c is 0.20 m³. The adiabatic constant of the gas is 1.60. The thermal efficiency of this engine is closest to A) 0.070. B) 0.10. C) 0.13. D) 0.16. E) 0.19.

Question

Quizplus · Accepted Answer

From the given cycle, it can be observed that the engine operates between two temperatures, 300 K and 500 K.

The efficiency of the Carnot cycle is given by 1 - Tc/Th, where Tc and Th are the temperatures of the cold and hot reservoirs, respectively. Therefore, the maximum possible efficiency of the engine is (1 - 300/500) = 0.4.

Since the engine operates on a reversible cycle, it can be assumed to be a Carnot engine, and its efficiency can be calculated as the ratio of the work done by the engine to the heat energy absorbed from the high-temperature reservoir, i.e.,

Efficiency = 1 - (Tc/Th) = 1 - (300/500)^(1.6/1.6) = 0.13

Therefore, the closest option is (C) 0.13.

A Heat Engine Performs the Reversible Cycle Abca with 9