Question

A Carnot engine working between two temperatures has efficiency of $40\%$. Whan the temperature of the sink is reduced by ${60}^{o}C$, the efficiency increases to $55\%$. Calculate the two temperature in the first case.

Answer 1

$T_2-$ Temperature of sink, $T_1-$ Temperature of source

Efficiency $=1-\frac{T_2}{T_1}=0.4Case\left(1\right)$ equation $1$

$1-\frac{(T_2-60)}{T_1}=0.55Case\left(2\right)$

$T_1-T_2+60=0.55T_1$

$T_2-0.45T_1=60$ equation $2$

Putting equation $2$ in $1$
$1-\frac{0.45T_1+60}{T_1}=0.4$

$⟹0.6T_1=0.45T_1+60$

$⟹T_1=400$ $K$

and $⟹T_2=240$ $K$