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Heat Capacity

The temperatu...

Question

The temperature of $1$ mole of ideal gas increase from $18^{o}$ to ${55.1}^{o}$ as the gas is compressed adiabatically. Calculate $q_{1}, W_{1}, Δ U, Δ H$ for this process assuming that $C_{V} = 3 / 2 R$ .

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Solution

$n = 1 m o l e;$ $T_{1} = 291 K;$ $T_{2} = 328.1 K$
Adiabatic process: $C_{V} = \frac{3}{2} R;$ $C_{P} = \frac{5}{2} R;$ $γ = \frac{5}{3}$

$W = \frac{n R Δ T}{γ - 1} = \frac{(1) (8.314) (37.1)}{\frac{5}{3} - 1} = \frac{3}{2} (8.3) (37.1)$
$\Rightarrow W = 461.865 J$

$q = 0$
$Δ U = n C_{V} Δ T = (1) (\frac{3}{2}) (37.1) = 50.6 J$
$Δ H = n C_{P} Δ T = (1) (\frac{5}{2}) (37.1) = \frac{185.5}{2} = 92.7 J$

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