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Heat Capacity

An ideal gas ...

Question

An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of $8000 g$ and an area of $5.00 c m^{2}$ and is free to slide up and down, keeping the pressure of the gas constant. How much work in Joules is done on the gas as the temperature of $0.200 m o l$ of the gas is raised from ${20.0}^{o} C$ to $300^{o} C$ ?

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Solution

First law of thermodynamics gives us the relation.
$q = Δ U + w$
$w = q - Δ U$
For a constant pressure process,
$q = n C_{p} Δ T$
$Δ U = n C_{v} Δ T$ (always)
Hence, $w = n (C_{p} - C_{v}) Δ T = n R Δ T = 0.2 \times 8.314 \times (300 - 20) = 466 J$

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