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Steam power plants are about 60% efficient according to the first law of thermodynamics, but engineers...

Steam power plants are about 60% efficient according to the first law of thermodynamics, but engineers tell the public that they are 90% efficient. Explain.

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Answer #1

First law of thermodynamics states that the heat energy we provide into a body will totally convert into internal energy and thermodynamic work. So First law efficiency will be defined as the amount of work done per unit of heat input, i.e,

η1st = W/Q

But the engineers talk about efficiency is not 1st law efficiency but the 2nd law efficiency.

2nd law states that due to increase in entropy there must be a waste heat and the desired work output from 1st law can not be achieved. Second Law efficiency tells that how much of the theoretical maximum efficiency you achieve. Basically it is the ratio of 1st law efficiency and carnot efficiency. So if we formulate 2nd law efficiency we get,

η2nd = η1st / ηcarnot

As the carnot efficiency is lesser than 1, the 2nd law efficiency will always be greater than 1st law efficiency. So if an engineer saying that the efficiency is 90% but the 1st law efficiency is 60% , he is talking about the 2nd law efficiency where he found out that the carnot efficiency is (60/90)*100 = 66%.

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