Question

Practical steam engines utilize 450ºC steam, which is later exhausted at 270ºC.

(a) What is the maximum efficiency that such a heat engine can have?
(b) Since 270ºC steam is still quite hot, a second steam engine is sometimes operated using the exhaust of the first.
(c) What is the maximum efficiency of the second engine if its exhaust has a temperature of 150ºC?

Answer 1

(a) 0.249 (24.9 %)

The maximum efficiency of a heat engine is given by

`\eta = 1-(T_C)/(T_H)`

where

Tc is the low-temperature reservoir

Th is the high-temperature reservoir

For the engine in this problem,

`T_C = 270^(\circ)C+273=543 K`

`T_H = 450^(\circ)C+273=723 K`

Therefore the maximum efficiency is

`\eta = 1-(T_C)/(T_H)=1-(543)/(723)=0.249`

(b-c) 0.221 (22.1 %)

The second steam engine operates using the exhaust of the first. So we have:

`T_H = 270^(\circ)C+273=543 K` is the high-temperature reservoir

`T_C = 150^(\circ)C+273=423 K` is the low-temperature reservoir

If we apply again the formula of the efficiency

`\eta = 1-(T_C)/(T_H)`

The maximum efficiency of the second engine is

`\eta = 1-(T_C)/(T_H)=1-(423)/(543)=0.221`