Question

The efficiency of a Carnot cycle is $\frac{1}{6}$. If on reducing the temperature of the sink by ${65}^o$ C, the efficiency becomes $\frac{1}{3}$.

Find the initial and final temperatures between which the cycle is working.

• A. $T_1=450Kand{T}_2=310K$
• B. $T_1=325Kand{T}_2=150K$
• C. $T_1=390Kand{T}_2=325K$
• D. $T_1=200Kand{T}_2=120K$

Answer 1

The correct option is C

$T_1=390Kand{T}_2=325K$

: If $T_1$ and $T_2$ are the temperatures of source and sink respectively, then

${\eta }_1=1-\frac{T_2}{T_1}$

or

$\frac{1}{6}=1-\frac{T_2}{T_1}$ .......(i)

When temperature of sink reduces by ${65}^o$ C, the ${\eta }_2=\frac{1}{3}$

$\therefore \frac{1}{3}=1-\frac{T_2-65}{T_1}$ .......(ii)

Solving equations (i) and (ii) we get

$T_1=390$K and $T_2=325$K