An ideal gas heat engine operates in a Carnot's cycle between $227^{\circ} \mathrm{C}$ and $127^{\circ}…
An ideal gas heat engine operates in a Carnot's cycle between $227^{\circ} \mathrm{C}$ and $127^{\circ} \mathrm{C}$. It absorbs $6 \times 10^{4}$ J at high temperature. The amount of heat converted into work is
$4.8 \times 10^{4} \mathrm{~J}$
$35 \times 10^{4} \mathrm{~J}$
$1.6 \times 10^{4} \mathrm{~J}$
$1.2 \times 10^{4} \mathrm{~J}$
Solution
Given, amount of heat absorbed, $Q=6 \times 10^{4} \mathrm{~J}$
Temperature of reservoir, $T_{1}=227^{\circ} \mathrm{C}=227+273 \mathrm{~K}$
$=500 \mathrm{~K}$
Temperature of $\operatorname{sink}, T_{2}=127^{\circ} \mathrm{C}$
$\begin{aligned}
&=127+273 \mathrm{~K} \\
&=400 \mathrm{~K}
\end{aligned}$
Efficiency of Carnot engine, $\eta=1-\frac{T_{2}}{T_{1}}$
$=1-\frac{400}{500}=\frac{1}{5}$
Work done by Carnot engine $(W)$
$\begin{aligned}
&=\text { Efficiency }(\eta) \times \text { heat absorbed }(Q) \\
W & {\left[\eta=\frac{W}{Q}\right] } \\
W &=\frac{1}{5} \times 6 \times 10^{4} \mathrm{~J}=1.2 \times 10^{4} \mathrm{~J}
\end{aligned}$