Question

An ideal gas heat engine operates in a Carnot's cycle between ${227}^{0}C$ and ${127}^{0}C$. It absorbs $6\times {10}^{4}J$ at high temperature. The amount of heat converted into work is:

• A. $1.6\times {10}^{4}J$
• B. $1.2\times {10}^{4}J$
• C. $4.8\times {10}^{4}J$
• D. $3.5\times {10}^{4}J$

Answer 1

The correct option is B $1.2\times {10}^{4}J$

Efficiency of a Carnot cycle $=\eta =$ $1-\frac{T_L}{T_H}=1-\frac{127+273}{227+273}$ $=1-\frac{400}{500}=1-\frac{4}{5}=\frac{1}{5}$

Thus $\frac{W}{Q}=\frac{1}{5}$

$⟹W=\frac{1}{5}\times 6\times {10}^{4}J=1.2\times {10}^{4}J$