An Inventor claims to have invented a heat engine that operates using energy res

Question

An Inventor claims to have invented a heat engine that operates using energy reservoirs that temperatures are 600 K and 300 K. She also claims that this engine provides 10 KW of power while rejecting heat at a rate of 2KW.

1) What is the rate at which heat is being transferred from a high temperature reservoir to this heat engine?

2) What is the rate at which the entropy of the low temperature reservoir is changing?

3) What is the rate at which work production is charging the entropy of the engine surroundings?

4) What is the rate at which entropy of the hot reservoir changes?

5) Does the system satisfy 2nd law? if so why?

Explanation / Answer

given T1 = 600 K and T2 = 300 K

power = heat supplied by hight temp reservoir - heat rejected to sink

10 KW = heat supplied by hight temp reservoir-2 KW

1) heat supplied by hight temp reservoir= 10 +2 = 12 KW

2) rate at which entropy of low temperature reservoir changing = heat rejected to sink/ temperature of sink = 2*103/300 = 20/3 J/sK = 20/3 *3600 = 24000 J/hrK = 24 KJ/hr K

3) rate at which work production is changing entropy of surroundings= 0

entropy change due to work production = zero.

4) rate at which entropy of high temparature reservoir changing = heat given by source/ temperature of source =- 12 *103 / 600 =-20 J/sK =20*3600 =72000 J/hr K =-72 KJ/hrK

5) the system satisfies 2nd law

It is impossible to construct a perfect heat engine which converts heat directly into work with out emitting heat to the environment.

here the engine works by emitting heat to low temp sink and produces power. Thus it satisfies second law.

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