First slide

Work done by gas

Question

The equation of a state of a gas is given by $ρ$ (V $-$ b) = nRT. 1 mol of a gas is isothermally expanded from volume V to 2V, the work done during the process is

Moderate

A

$R T \ln (\frac{2 V - b}{V - b})$
B

$R T \ln (\frac{V - b}{V})$
C

$R T \ln (\frac{V - b}{2 V - b})$
D

$R T \ln (\frac{V}{V - b})$

Solution

$p = \frac{n R T}{V - b}$
$W = \int_{V}^{2 V} p d V = n R T \int_{V}^{2 V} \frac{d V}{V - b} (As, T = constant)$
$= n R T \ln (\frac{2 V - b}{V - b}) = R T \ln (\frac{2 V - b}{V - b}) (As, n = 1)$

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