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A heat engine operates between a cold re...

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 could be the minimum tempreture of the hot reservior ?

Text Solution

Verified by Experts

The work done by the engine in a cycle is
`W=200 J-120 J=80 J`.
the efficiency of the engine is
`eta =(W)/(Q)=(80 J)/(200 J)=0.40`.
From carnot's theorem, no engine can have an efficiency greater than that of a carnot engine.
Thus, `0.40le 1 -T_(2)/T_1=(1)-(300 K)/(T_(1)`
or, `(300 K)/(T_(1)le 1-0.40=0.60`
or,`T_(1)ge(300 K)/(0.60)`
or, `T_(1)ge500 K`.
The minimum tempreture of the hot reservoir has to be 500 K.
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