Question

Two Carnot engines operate in series such that the heat rejected from one is the heat input to the other. The heat transfer from the high-temperature reservoir is 500 kJ. The overall temperature limits are 1000K and 400K. Both engines produce equal work. What is most nearly the intermediate temperature between the two engines?

Answer 1

Answer:

Given:

high temperature reservoir $T_{H} =1000k$

low temperature reservoir $T_{L} =400k$

thermal efficiency $n_{1}= n_{2}$

The engines are said to  operate on Carnot cycle which is totally reversible.

To find the intermediate temperature between the two engines, The thermal efficiency of the first heat engine can be defined as

$n_{1} =1-\frac{T}{T_{H} }$

The thermal efficiency of second heat engine can be written as

$n_{2} =1-\frac{T_{L} }{T}$

The temperature of intermediate reservoir can be defined as  

$1-\frac{T}{T_{H} } =1-\frac{T_{L} }{T} \\T^2=T_{L} T_{H} \\T=\sqrt{T_{L} T_{H} }\\T=\sqrt{400*1000} =632k$