Question

$P-V$ plots for two gases during adiabatic processes are shown in the figure. Plots $1$ and $2$ should correspond respectively to

• A. $\text{He and}{\text{O}}_2$
• B. ${\text{O}}_2\text{and}\text{He}$
• C. $\text{He}\text{and}\text{Ar}$
• D. ${\text{O}}_2\text{and}{\text{N}}_2$

Answer 1

The correct option is B ${\text{O}}_2\text{and}\text{He}$

For monoatomic gas, $\gamma =\frac{5}{3}=1.67$
For diatomic gas, $\gamma =\frac{7}{5}=1.4$

$\Rightarrow {\gamma }_{monoatomic}>{\gamma }_{diatomic}$

For an adiabatic process,
$P{V}^{\gamma }=\text{Constant}$

$\Rightarrow P\propto \frac{1}{V^{\gamma }}$


For a given $V$, lower the value of $\gamma$, higher will be the value of $P$.

As, curve $\left(1\right)$ will have higher $P$ for a given $V$,

Curve $\left(1\right)$ will be a diatomic gas $\left({\text{O}}_2\right)$ and curve $\left(2\right)$ will be a monoatomic $\left(\text{He}\right)$ gas.

Hence, option $\left(B\right)$ is correct.

Why this question? Key concept: For $P{V}^{\gamma }=\text{constant}$, in $P-V$ graph, higher the value of $\gamma$, higher the slope.