Question

The efficiency of carnot engine is $50\%$ and temperature of sink is $500\text{K}$. If temperature of source is kept constant and its efficiency raised to $60\%$, then required temperature of the sink will be:

• A. $100\text{K}$
• B. $600\text{K}$
• C. $400\text{K}$
• D. $500\text{K}$

Answer 1

The correct option is C $400\text{K}$

Given that
Efficiency $\left({\eta }_1\right)=50\%$ & Sink temperature $\left(T_2\right)=500\text{K}$ and ${\eta }_2=60\%\&T_2^{\prime }=?$
From formula, efficiency $\left(\eta \right)$ of carnot cycle
$\eta =(1-\frac{T_2}{T_1})\times 100\%$
$\Rightarrow \frac{50}{100}=1-\frac{500}{T_1}$
$\Rightarrow T_1=1000\text{K}$ ...........(1)
for ${\eta }_2=60\%$
$\frac{60}{100}=1-\frac{T_2^{\prime }}{1000}\Rightarrow T_2^{\prime }=400\text{K}$
Hence, option $\left(c\right)$ is the correct answer.