Question

A heat engine takes in 125 kJ of heat from a reservoir at 815 K and exhausts 85.0 kJ to a reservoir at 292 K. What is the efficiency of the engine?

Answer 1

We are given the following data :

Now, the efficiency of any heat engine is given by the work done by the heat engine per unit heat taken from the hot reservoir.

To get the efficiency we need to find the work done by the heat engine.

Assuming that the heat is not lost by any other means other than work, the work done will be equal to

So, using in (1)

So, using the values of and , we get the efficiency

Which is the required efficiency.

BONUS

By looking at the question I see that the reservoir temperatures are also provided. So, I am guessing that the efficiency of an ideal engine operating between the same two reservoirs was also asked / will be asked. So, I am solving that too below.

The efficiency of an ideal engine operating between two reservoirs with temperatures and is given by

Using the values provided, we get

Notice that the efficiency of an ideal heat engine is much more than the efficiency calculated before although the two heat engines work between the same two temperatures. By definition, an ideal engine always has the maximum efficiency for any value of and .

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