A Carnot engine whose sink is at 300 K has an efficiency of 40%. By howmuch should the
temperature of source be increased so as to increase its efficiency by 50% of original
efficiency ?

250 K

\(\eta = 1 - \frac{T_2}{T_1}\)

\(\eta = 0.4 \text{ ; } T_2 = 300  K \)

⇒ T₁ = 500 K

now \(\eta' = 0.4 + 0.4 × \frac{50}{100} = 0.6\)

\(\eta' = 1 - \frac{T_2}{T_1 + \Delta T}\)

⇒ \(\Delta T = 250 K\)