First slide

Work done by gas

Question

A monoatomic gas is supplied the heat Q very slowly keeping the pressure constant. The work done by
the gas will be

Moderate

A

$\frac{2}{3} Q$
B

$\frac{3}{5} Q$
C

$\frac{2}{5} Q$
D

$\frac{1}{5} Q$

Solution

$Δ Q = Δ U + Δ W$
$\Rightarrow Δ W = (Δ Q)_{p} - (Δ U)_{V} = (Δ Q)_{p} [1 - \frac{(Δ U)_{V}}{(Δ Q)_{p}}]$
$= (Δ Q)_{p} [1 - \frac{C_{V}}{C_{p}}] = Q [1 - \frac{3}{5}] = \frac{2}{5} Q$
$(∵ (Δ Q)_{p} = Q and γ = \frac{5}{3} for monoatomic gas)$

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