One mole of a van der Waals gas expands reversibly and isothermally at from 2 L to 20 L. The magnitu — Thermodynamics and Thermochemistry Chemistry Question
Question
One mole of a van der Waals gas expands reversibly and isothermally at $27^\circ\text{C}$ from 2 L to 20 L. The magnitude of work done (in J) if $a = 1.42 \times 10^{12}\text{ dynes cm}^4\text{/mole}$ and $b = 30\text{ ml/mole}$.
Answer: 5778
💡 Solution & Explanation
$W = \int P dV = \int_{V_1}^{V_2} \left( \frac{RT}{V-b} - \frac{a}{V^2} \right) dV = RT \ln\left(\frac{V_2-b}{V_1-b}\right) + a\left(\frac{1}{V_2} - \frac{1}{V_1}\right)$. Substituting standard converted values for $a$ and $b$ strictly evaluates the magnitude of work done to 5778 J.
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