Question

The $P-V$ plots for two gases each undergoing an adiabatic process are as shown in the figure. The graphs 1 and 2 can correspond to :-

• A. $O_2$ and $He$
• B. $He$ and $O_2$
• C. $O_2$ and $CO$
• D. $N_2$ and $O_2$

Answer 1

The correct option is A $O_2$ and $He$

Slope of $P-V$ curve in an adiabatic process is given by
$\frac{dP}{dV}=\frac{-\gamma P}{V}$
For a particular value of $P$ and $V$, we can say that, more the $\gamma$ value, more is the slope and vice versa.


Slope of graph of any two diatomic or monoatomic gases will be the same, as they have same values of $\gamma$.
So, we can conclude that options (c) and (d) are wrong.
From the given graph, we can say that at the common point (same $P,V$), graph 2 has a higher slope and graph 1 has lower slope.
That implies, $\gamma$ value of the gas in graph 1 is less than the $\gamma$ value of the gas in graph 2.
But we know that, ${\gamma }_{dia}<{\gamma }_{mono}$
Hence, graph 1 and graph 2 can represent adiabatic curves for a diatomic and monoatomic gas respectively.
Thus, option (a) is the correct answer.