Question

Four moles of an ideal gas at ${27}^{\circ }\text{C}$ is allowed to expand isothermally from an initial pressure of $12.0\text{atm}$ to a final pressure of $6.0\text{atm}$ against a constant external pressure of $1.0\text{atm}$. Thus, work done will be

• A. $-1870.6\text{J}$
• B. $+1870.6\text{J}$
• C. $-18.47\text{J}$
• D. $-831.4\text{J}$

Answer 1

The correct option is D $-831.4\text{J}$

Gas is being expanded against external pressure. Thus, work is done by the system, work is negative.
$W=-P_{\text{ext}}[V_2-V_1]$
$=-P_{\text{ext}}[\frac{nRT}{P_2}-\frac{nRT}{P_1}]=-nRT{P}_{\text{ext}}[\frac{1}{P_2}-\frac{1}{P_1}]$
$=-4\text{mol}\times 0.0821{\text{L atm mol}}^{-1}{\text{K}}^{-1}\times 1[\frac{1}{6}-\frac{1}{12}]\times 300\text{K}$
$=-8.21\text{L atm}=\frac{-8.21\text{L atm}\times 8.314\text{J}}{0.0821\text{L atm}}=-831.4\text{J}$