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

Question No. 154 Mechanical | GATE 2016

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} $

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