Question

A Carnot engine whose hot-reservoir temperature is 400 ∘C has a thermal efficiency of 45 % . By how many degrees should the temperature of the cold reservoir be decreased to raise the engine's efficiency to 58 % ?

Answer 1

Efficiency of carnot engine $\eta$ = 1 - ( Tc / Th )

hot-reservoir temperature Th =  400 ∘C

0.45 = 1 - [ Tc / (400+2730) ]

Tc = 370.15 K ----------------------(1)

Now to get the efficiency 58%

0.58 = 1 - [ Tc / (400+273) ]

Tc = 282.66 K -------------------(2)

So from (1) and (2) it clear that

temperature should be decreased by

370.15 - 282.66 = 87.49 ∘C

Good Luck !