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 [tex]T_C[/tex] and hot temperature [tex]T_H[/tex] is given by
[tex]\eta = 1 - \frac{T_C}{T_H} [/tex]
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, [tex]T_C=270 K[/tex] and [tex]T_H=710 K[/tex], the efficiency is
[tex]\eta = 1 - \frac{270 K}{710 K}=0.62 = 62% [/tex]
Therefore, the correct answer is D) 62 %.
