A sample of ideal gas $(γ = 1.4)$ is heated at constant pressure. If an amount of heat $140 J$ is supplied to the gas, find the work done by the gas?

100 J

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40 J

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180 J

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60 J

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Solution

The correct option is B $40 J$
Let n be the no of moles of the gas.
Let the temp changes from $T_{1}$ to $T_{2}$ and volume from $V_{1}$ to $V_{2}$ respectively.

Heat supplied: $Q = n C_{p} (T_{2} - T_{1}) = 140$
Change in internal energy: $Δ U = n C_{v} (T_{2} - T_{1}) = n \frac{C_{p}}{γ} (T_{2} - T_{1}) = \frac{140}{1.4} = 100 J$
Work done by the gas: $Δ Q - Δ W = 140 - 100 = 40 J$

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