What is the maximum efficiency of a heat engine whose operating temperatures are 570°C and 360°C?

Answer 1

the efficiency is given by

E= (Tw-Tc)/Tw

where T is absolute temperature , w for warm, c for cold
Tw= 570+273=843K , Tc=273+360 = 633

so E = (843-633)/843=0.249= 24.9%

Answer 2

Efficiency of heat engines is derived as follows:

Heat Qh coming from hot reservoir of absolute temperature Th contains entropy Sh = Qh/Th
Heat Qc dumped to cold reservoir of absolute temperature Tc contains entropy Sc = Qc/Tc

Second law of termodynamics:
Sc > Sh
Qc/Tc > Qh/Th
when absolute temperatures are positive
Qc > Tc/Th Qh

First law of termodynamics:
work = Qh - Q2c
work < Qh - Tc/Th Qh
work < (1 - Tc/Th) Qh
efficiency = work/Qh < (1 - Tc/Th)