Question

A cylinder fixed with a piston contains saturated vapour of a refrigerant at ${10}^{\circ }C,$ the volume and pressure are $10\text{L}$ and $0.681\text{MPa}$ respectively. The refrigerant is compressed to $3.5\text{L}$ and $2\text{MPa}$. If the saturated vapour is undergoing polytropic process as $P{V}^n=$ constant, where $n=1.025,$ then calculate the work done during the process.

• A. $-7.60\text{kJ}$
• B. $-5.76\text{kJ}$
• C. $-3.12\text{kJ}$
• D. $-2.9\text{kJ}$

Answer 1

The correct option is A $-7.60\text{kJ}$

Given,$P_1=681\text{kPa};V_1=10\times {10}^{-3}{\text{m}}^3$
$P_2=2000\text{kPa};V_2=3.5\times {10}^{-3}{\text{m}}^3$
Equation of state of polytropic process is given as $P{V}^{1.025}=$ constant.
$\because$ In a polytropic process, work done is given by
$W=\frac{P_1{V}_1-P_2{V}_2}{n-1}$
From the given data we get,
$W=\frac{681\times 10-2000\times 3.5}{0.025}=-7.60\text{kJ}$
Thus, option (a) is the correct answer.