Consider three engines that each use 2120 J of heat from a hot reservoir (temper
ID: 1794386 • Letter: C
Question
Consider three engines that each use 2120 J of heat from a hot reservoir (temperature = 530 K). These three engines reject heat to a cold reservoir (temperature = 325 K). Engine I rejects 1300 J of heat. Engine II rejects 1531 J of heat. Engine III rejects 655 J of heat. One of the engines operates reversibly, and two operate irreversibly. However, of the two irreversible engines, one violates the second law of thermodynamics and could not exist. For each of the engines determine the total entropy change of the universe, which is the sum of the entropy changes of the hot and cold reservoirs. On the basis of your calculations, identify which engine operates reversibly, which operates irreversibly and could exist, and which operates irreversibly and could not exist. (Round off to two decimal places.)
S (J/K) Type of operation
Engine 1 ??? reversible/irreversible could exist/irreversible could not exist
Engine 2 ??? reversible/irreversible could exist/irreversible could not exist
Engine 3 ??? reversible/irreversible could exist/irreversible could not exist
Explanation / Answer
In all cases, the hot reservoir transfers 2120J of thermal energy to the engine at a temperature of 530K. The change in thermal energy of the hot reservoir, q_hot, is -2120J, and the change in entropy of the hot reservoir is S = q/T = (-2120J)/(530K) = -4 J/K.
The engines add thermal energy to the cool reservoir at at temperature of 325K. The entropy changes of the cool reservoir due to the three engines is therefore:
Engine 1: q/T = (1300J)/(325K) = +4 J/K
Engine 2: q/T = (1531J)/(325K) = +4.71 J/K
Engine 3: q/T = (655J)/(325K) = +2.02 J/K
The change in entropy of the universe is the sum of the changes in the hot and cold reservoirs:
Engine 1: S = (4.00 - 4.00)J/K = 0 J/K
Engine 2: S = (4.71 - 4.00)J/K = 0.71 J/K
Engine 3: S = (2.02 - 4.00)J/K = -1.98 J/K
The first engine operates reversibly (the change in entropy of the universe is zero).
For second engine the entropy change of the universe is 0.71 J/K. This engine can exist therefore and is irreversible due to the increase in the universes entropy.
The third engine violates the 2nd law because the entropy of the universe would decrease. It is therefore not a physically realizable engine.