Question

Work done on $3$ moles of an ideal gas at $27^{\circ} C$, if it is compressed reversibly and isothermally from a pressure of $1.01 \times 10^{5} N m ^{-2}$ to $5.05 \times 10^{6} N m ^{-2}$ is______ $kJ$.
[Given $\log _{10}(2)=0.3010$]

Answer 1

For reversible process under isothermal conditions,
$w =-2.303\, nRT \log _{10} \frac{ P _{1}}{ P _{2}}$
$=-2.303 \times 3 \times 8.314 \times 300 \log _{10} \frac{1.01 \times 10^{5}}{5.05 \times 10^{6}} $
$=-2.303 \times 3 \times 8.314 \times 300 \times \log _{10}\left(2 \times 10^{-2}\right)$
$=2.9277 \times 10^{4}\, J =29.28\, kJ$