A heat engine operates between a cold reservoir at tempreture `T_(2)=300 K` and a hot reservior at tempreture `T_(1)`. It takes `200 J` of heat from the hot reservior and delivers `120 J` of heat to the cold reservior in a cycle. What sould be the minimum temperature of the hot reservior ?

Answer

`500K`

Explanation

Work done by the engine in one cycle
`W=Q_(1)-Q_(2)= 200-120= 80J`
`eta=W/(Q_(1))=(80)/(200)= 0.40`
Acoording to Carnot theorem, no engine can have efficiency greater than that of Carnot engine.
`:. 0.40le(1-(T_(2))/(T_(1)))= 1-(300)/(T_(1))`
or `(300)/(T_(1))le 1-0.40=0.60`
`:. T_(1)ge(300)/(0.6)= 500K`.
Hence, minimum temp.of hot reservoir is
`T_(1)=500K`