MCQ
A carnot engine has the same efficiency between $800 K$ to $500 K$ and $x K$ to $600 K$. The value of $x$ is
- A$1000 \mathrm{~K}$
- ✓$960 K$
- C$846 K$
- D$754 K$
✓
Answer
Correct option: B.
$960 K$
In first case, $\left(\eta_1\right)=1-\frac{500}{800}=\frac{3}{8}$ and
in second case, $\left(\eta_2\right)=1-\frac{600}{x}$
Since $\eta_1=\eta_2$, therefore $\frac{3}{8}=1-\frac{600}{x}$
$\text { or } \frac{600}{x}=1-\frac{3}{8}=\frac{5}{8}$
$\text { or }x=\frac{600 \times 8}{5}=960 \mathrm{~K}$
in second case, $\left(\eta_2\right)=1-\frac{600}{x}$
Since $\eta_1=\eta_2$, therefore $\frac{3}{8}=1-\frac{600}{x}$
$\text { or } \frac{600}{x}=1-\frac{3}{8}=\frac{5}{8}$
$\text { or }x=\frac{600 \times 8}{5}=960 \mathrm{~K}$
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