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:

  1. 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 $He(\gamma=1.67)$.



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