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Derive the formula for the efficiency of carnot heat engine and explain it.

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For a heat engine, the total thermodynamical process is generally irreversible. The ratio of work done to convert heat and the heat absorbed by the source is called efficiency.

This means that,

From the above relation, it is clear that the efficiency of engine depends upon the temperature of source (T1) and sink (T2).
Here T1 > (T1 – T2). Efficiency is always less than one, i. e., less than 100%.

If T1 = T2, then η = 0, which represents that when source and sink are at same temperature. Then, in this situation, heat energy can not be transformed to mechanical energy. It is to be noted here that the value of q will be 100% in two situations: if T1 = ∞ or T2 = 0, and both these situations are not possible. So, efficiency can not be 100%.

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