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, $0.5=1-\frac{T_2^{{}^{\prime }}}{T_1^{{}^{\prime }}}$
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
$T_1^{{}^{\prime }}=2T_1,T_2^{{}^{\prime }}=2T_2$