Question

The input to, and outputs from, three heat engines are listed below. If the temperatures of the hot and cold reservoirs are TH = 600K and TC = 300K in each case, determine for each engine if laws of energy conservation and maximum engine efficiency and are obeyed.

(1) Heat in QH = 50J, Heat out QC = 20J, and Work out Wout = 30J

(2) Heat in QH = 10J, Heat out QC = 7J, and Work out Wout = 4J.

(3) Heat in QH = 30J, Heat out QC = 10J, and Work out Wout = 20J.

Answer 1

efficiency is given as

= 1 - (T_c/T_h) = 1 - (300/600) = 0.5

1)

laws of energy conservation is obeyed since

Q_h = Q_c + W_out   :             50 = 20 + 30 = 50

maximum engine efficiency is not obeyed

since = 1 - (Q_c/Q_h) = 1 - (20/50) = 0.6

2)

laws of energy conservation is not obeyed since

Q_h < Q_c + W_out   :             10 < 7 + 4 = 11

maximum engine efficiency is not obeyed

since = 1 - (Q_c/Q_h) = 1 - (7/10) = 0.3

c)

laws of energy conservation is obeyed since

Q_h = Q_c + W_out   :             30 = 10 + 20 = 50

maximum engine efficiency is not obeyed

since = 1 - (Q_c/Q_h) = 1 - (10/30)