# GATE Papers >> Mechanical >> 2016 >> Question No 154

Question No. 154

A piston-cylinder device initially contains $0.4\;\mathrm m^3$ of air (to be treated as an ideal gas) at 100 kPa and $80\;{}^\circ\mathrm C$. The air is now isothermally compressed to $0.1\mathrm m^3$. The work done during this process is ________ kJ.

(Take the sign convention such that work done on the system is negative)

##### Answer : -55.6 : -55.4

Solution of Question No 154 of GATE 2016 Mechanical Paper

Given data: ${\mathrm V}_1=0.4\mathrm m^3$

$\begin{array}{l}{\mathrm P}_1=100\mathrm{kPa}\\{\mathrm T}_1=80+273\mathrm K=353\mathrm K\\{\mathrm V}_2=0.1\mathrm m^3\\\mathrm{Work}\;\mathrm{done}={\mathrm P}_1{\mathrm V}_1\ln\frac{{\mathrm V}_2}{{\mathrm V}_1}\;\;(\mathrm{Isothermal})\\=100\times0.4\;\ln\left(\frac{0.1}{0.4}\right)=-55.45\mathrm{kJ}\end{array}$