Question

A Carnot engine is operated between constant temperature reservoirs, T_C and T_H. The operator wishes to increases the efficiency of the engine. If only one reservoir can be changed by a given amount for either reservoir, which is better: lowering the cold reservoir or raising the hot reservoir? (Hint: Think about how the efficiency changes when you change one of the two temperature reservoirs.)

Answer 1

Efficiency of a carnot engine is given by,  

For example, let TC = 20 K and TH = 100 K , efficiency   

Now, if TC is decreased, say to 10 K, and TH remains 100 K, then new efficiency is

efficiency is more than initial case

Now, if TH is increased, say to 110 K, and TC remains 20 K, then new efficiency​​​​​​​ is

efficiency is more than initial case (but less than the second case)

Hence, lowering the cold reservoir temperature gives greater efficiency