Question

The efficiency of Carnot's heat engine is $0.5$ when the temperature of the source is $T_{1}$ and that of sink is $T_{2}$ . The efficiency of another Carnot's heat engine is also $0.5$ . The temperature of source and sink of the second engine are respectively :-

• A. $2T_{1},2T_{2}$
• B. $2T_{1},\frac{T_{2}}{2}$
• C. $T_{1}+5,T_{2}-5$
• D. $T_{1}+10,T_{2}-10$

Answer 1

Answer: (A)

Efficiency of Carnot's heat engine,
$\eta=1-\frac{T_{2}}{ T_{1}}$
For first Carnot's heat engine, $0.5=1-\frac{T_{2}}{ T_{1}}$
For second heat engine, $0.5=1-\frac{T_{2}^{'}}{T_{1}^{'}}$
Efficiency remains the same when both $T_{1}$ and $T_{2}$ are increased by same factor Therefore, the temperature of source and sink of second engine are
$T_{1}^{'}=2T_{1},T_{2}^{'}=2T_{2}$