Heat and Thermodynamics 5 Question 22
23. $p-V$ plots for two gases during adiabatic processes are shown in the figure. Plots 1 and 2 should correspond respectively to
(2001, 2M)
(a) $He$ and $O _2$
(b) $O _2$ and $He$
(c) He and Ar
(d) $O _2$ and $N _2$
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Solution:
- In adiabatic process
slope of $p-V$ graph, $\frac{d p}{d V}=-\gamma \frac{p}{V}$
$$ \text { slope } \propto \gamma $$
(with negative sign)
From the given graph,
$$ (\text { slope }) _2>(\text { slope }) _1 $$
$$ \therefore \quad \gamma _2>\gamma _1 $$
Therefore, 1 should correspond to $O _2(\gamma=1.4)$ and 2 should correspond to $He(\gamma=1.67)$.
