Question

Derive the expression for work when a gas expands against constant external pressure.

Answer 1

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Answer 2

Explanation :

Derivation for the expression for work when a gas expands against constant external pressure. That means,

By the definition of the work involved is given by :

$w=-(\text{External force})(\text{Distance through which piston moves})$

$w=-(\frac{\text{Force}}{\text{Area of cross-section of piston}})\times (\text{Area of cross-section of piston})\times \\\\(\text{Distance through which piston moves})$

$w=-p_{ext}\times (\Delta V)$

where, $\Delta V$ is the change in the volume of the system. If the piston moves by an infinitesimal amount, the work involved is give by,

$\delta w=-p_{ext}\times (dV)$

The total work involved during the change of volume from $V_1$ to $V_2$  can be obtained by integrating the above expression, we get

$w=-\int_{V_1}^{V_2}p_{ext}\times dV\\\\w=-p_{ext}(V_2-V_1)$