Question

A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of and performs 4.1 kJ of net work, and rejects of heat, in a single cycle. What is thermal efficiency of a Carnot heat engine, operating between the same heat reservoirs?

37%

43%

50%

62%

56%

Answer 1

There are some missing data in the problem. The full text is the following:
"A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of 710 K and 270 K performs 4.1 kJ of net work, and rejects 9.7 kJ of heat, in a single cycle. The thermal efficiency of a Carnot heat engine, operating between the same heat reservoirs, in percent, is closest to.."

Solution:
The efficiency of a Carnot cycle working between cold temperature
`T_C` and hot temperature
`T_H` is given by

`\eta = 1 - (T_C)/(T_H)`
and it represents the maximum efficiency that can be reached by a machine operating between these temperatures. If we use the temperatures of the problem,
`T_C=270 K` and
`T_H=710 K`, the efficiency is

`\eta = 1 - (270 K)/(710 K)=0.62 = 62%`

Therefore, the correct answer is D) 62 %.