Acarnot heat engine receives 600 kj of heat from a source of unknown temperature and rejects 175 kj of it to a sink at 20°c. determine (a) the temperature of the source and (b) the thermal efficiency of the heat engine.

(b) 71%

The thermal efficiency of a Carnot heat engine is given by:

where

W is the useful work done by the engine

is the heat in input to the machine

In this problem, we have:

is the heat absorbed

is the work done (175 kJ is the heat released to the sink, therefore the work done is equal to the difference between the heat in input and the heat released)

So, the efficiency is

(a)

The efficiency of an engine can also be rewritten as

where

is the absolute temperature of the cold sink

is the temperature of the source

In this problem, the temperature of the sink is

So we can re-arrange the equation to find the temperature of the source:

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