Question

A Carnot engine whose low-temperature reservoir is at 15.7°C has an efficiency of 22.9%. By how much should the Celsius temperature of the high-temperature reservoir be increased to increase the efficiency to 63.5%?

Answer 1

Given data:
low-temperature reservoir is at 15.7°C
efficiency of 22.9%
increase the efficiency to 63.5%
The carnot efficiency is defined as e = 1 - Tc/Th where Tc is the temperature of the cold reservoir, and Th is the temperature of the hot (both measured in Kelvin).

15.7 degrees C = 288.7 K

So, solving for Th
Tc/Th = 1-e = 1-0.229=0.771
Th =   288.7/0.771=374.44 K

You want to make e = 0.635, so you need to solve for the Th that can do this, given that Tc is fixed at 288.7 K.

0.635 = 1-Tc/Th
0.365 = Tc/Th
Th = 288.7/0.635= 454.6 K

So, you need to increase the temperature of the hot source by about 454.6-374.44=80.19 K.