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?

(a) 0.249 (24.9 %)

The maximum efficiency of a heat engine is given by

where

Tc is the low-temperature reservoir

Th is the high-temperature reservoir

For the engine in this problem,

Therefore the maximum efficiency is

(b-c) 0.221 (22.1 %)

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

is the high-temperature reservoir

is the low-temperature reservoir

If we apply again the formula of the efficiency

The maximum efficiency of the second engine is

at right angles to each other