Question

A perfect Carnot engine utilises an ideal gas and works between the temperatures ${227}^{o}C$ and ${127}^{o}C$. If work output of the engine is ${10}^4$, then the amount of heat rejected to the sink will be

• A. $1\times {10}^{4}Joule$
• B. $3\times {10}^{4}Joule$
• C. $5\times {10}^{4}Joule$
• D. $4\times {10}^{4}Joule$

Answer 1

Answer: (D)

$4\times {10}^{4}Joule$

Efficiency of a Carnot engine = $\eta =1-\frac{T_{sink}}{T_{source}}$

So, $\eta =1-\frac{400}{500}=\frac{1}{5}$

$\eta =\frac{W}{Q_{source}}$

So, $Q_{source}=5\times {10}^4$ J

$\frac{T_{sink}}{T_{source}}=\frac{Q_{sink}}{Q_{source}}=\frac{4}{5}$

So, $Q_{sink}=4\times {10}^4$