Three designs are proposed for an engine which is to operate between $500 \mathrm{~K}$ and $300 \mathrm{~K}$…
Three designs are proposed for an engine which is to operate between $500 \mathrm{~K}$ and $300 \mathrm{~K}$. Design A claims to produce $150 \mathrm{~J}$ of work per $1000 \mathrm{~J}$ of heat input, design $B 450 \mathrm{~J}$ of work per $1000 \mathrm{~J}$ and design $C 300 \mathrm{~J}$ of work per $1000 \mathrm{~J}$. Which of the design would you choose?
A
B
C
None is suitable
Solution
Given, temperature, $T_1=500 \mathrm{~K}, T_2=300 \mathrm{~K}$
Efficiency of the engine, $\eta=1-\frac{T_2}{T_1}$
$
\begin{array}{ll}
\Rightarrow & \eta=1-\frac{300}{500} \\
\Rightarrow & \eta=\frac{2}{5}=0.4
\end{array}
$
For design A, work done = 150 J
Heat input = 1000 J
$\begin{aligned} \text { Efficiency of design } A & =\frac{\text { Work done }}{\text { Heat input }} \\ & =\frac{150}{1000}=0.15\end{aligned}$
For design B, work done = 450 J
Heat input = 1000 J
$\begin{aligned} \text { Efficiency of design } B & =\frac{\text { Work done }}{\text { Heat input }} \\ & =\frac{450}{1000}=0.45\end{aligned}$
For design C, work done = 300 J
Heat input = 1000 J
Efficiency of design $\begin{aligned} C & =\frac{\text { Work done }}{\text { Heat input }} \\ & =\frac{300}{1000}=0.3\end{aligned}$
Hence, design B is most suitable as its efficiency is almost equal to efficiency of given engine