Question

A mass of gas is compressed in a quasi-static process from 80 kPa, $0.1m^{3}to0.4MPa,0.03m^3.$ Assuming that the pressure and volume are related by $P{V}^n=$ constant. The work done by the gas system is

• A. $-11.83kJ$
• B. $-3.8kJ$
• C. $-7.4kJ$
• D. $-23.2kJ$

Answer 1

The correct option is A $-11.83kJ$

$\begin{array}{cc}P{V}^n& =constant\\ P_1{V}_1^n& =P_2{V}_2^n\\ 80\times (0.1{)}^n& =400\times (0.03{)}^n\\ \therefore n& =1.34\\ W& =\frac{P_1{V}_1-P_2{V}_2}{n-1}\\ & =\frac{80\times 0.1-400\times 0.03}{1.34-1}=-11.8kJ\end{array}$