Question

One $\text{mole}$ of a gas in a cylinder is compressed from $8{\text{m}}^3$ to $2{\text{m}}^3$ quasi-statically at a constant temperature of $300\text{K}$. Workdone during this process is
($\ln 2=0.693$)

• A. $3455\text{J}$
• B. $-3455\text{J}$
• C. $1728\text{J}$
• D. $-1728\text{J}$

Answer 1

The correct option is B $-3455\text{J}$

Given,
Initial volume $\left(V_i\right)=8{\text{m}}^3$
final volume $\left(V_f\right)=2{\text{m}}^3$
Temperature (T) $=300\text{K}$
Work done during an isothermal process, $\left(W\right)=\text{nRT ln}\left(\frac{V_f}{V_i}\right)$
$W=8.31\times 300\times \ln \left(\frac{2}{8}\right)$
$=-8.31\times 300\times \ln \left(4\right)$
$\approx -3455\text{J}$