Question

2 mole of a ideal gas at 2 bar and 27 deg celcius expands isothermally against a constant pressure of 1 bar. the work done by the gas is equal to

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{w}=-\mathrm{nRTln}\left(\frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}\right) \\ \mathrm{Here},\mathrm{n}=2 \\ \mathrm{R}=8.314{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1} \\ \mathrm{T}=27°\mathrm{C}=27+273=300\mathrm{K} \\ {\mathrm{P}}_1=2\mathrm{bar} \\ {\mathrm{P}}_2=1\mathrm{bar} \\ \mathrm{Therefore}, \\ \mathrm{w}=-\left(2\right)(8.314)\left(300\right)\ln \frac{2}{1} \\ \mathrm{or},\mathrm{w}=(-2)(8.314)\left(300\right)\left(\ln 2\right)=-3457.69\mathrm{J}=-34.57\mathrm{kJ} \end{gathered}$$