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First Law of Thermodynamics

Calculate ent...

Question

Calculate enthalpy change (in kcal) in adibatic compression of 5 moles ideal triatomic non-linear gas against a constant external pressure of $2 a t m$ starting from initial pressure of $1 a t m$ and initial temperature of $300 K$ :
(Given R= 2 cal/mol.K and vibrational degrees of freedom are inactive)

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Solution

Since we are taking an adibatic process, so from the first law of thermodynamics,
$Δ U = W$
$\Rightarrow n C_{v} (T_{2} - T_{1}) = - P_{e x t} (V_{2} - V_{1})$
Since it is a triatomic non linear system, hence
$\Rightarrow n C_{v} (T_{2} - T_{1}) = P_{e x t} (V_{2} - V_{1})$ $\Rightarrow n 3 R (T_{2} - 300) = - 2 (\frac{n R T_{2}}{2} - \frac{n R 300}{1})$
$\Rightarrow 3 T_{2} - 900 = - T_{2} + 600$
$\Rightarrow T_{2} = 375 K$
We know, $Δ H = n C_{p} Δ T = 5 \times 4 \times 2 (375 - 300) = 3000 c a l = 3 k c a l$

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