A heat engine operates between a cold reservoir at temperature `T_2=300K` and a hot reservoir at temperature `T_1`. It takes 200 J of heat from the hot reservoir and delivers 120 J of heat from the hot reservoir and delivers 120 J of heat to the cold reservoir in a cycle. What could be the minimum temperature of the hot reservoir?

Explanation

Work done by the engine in a cycle is `W=200-120 = 80J eta =(W)/(Q) = (80)/(200) = 0.4`
From carnot's Theorem ` 0.4 le 1 - (T_(2))/(T_(1)) = 1 - (300)/(T_(1)) implies (300)/(T_(1)) le 0.6 implies T_(1) ge (300)/(0.6) implies T_(1) ge 500`