Question

Assertion :The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning). Reason: The atoms of a monoatomic gas have less degree of freedom as compared to molecules of the diatomic gas.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

If $f$ be the degree of freedom, then the ratio
$\frac{C_p}{C_v}=\gamma$ is given by $\gamma =1+\frac{2}{f}$
For monoatomic gas, $f=3$
$\therefore$ $\gamma =1+\frac{2}{3}=\frac{5}{3}=1.67$
For diatomic gas $f=5$
$\therefore$ $\gamma =1+\frac{2}{5}=\frac{7}{5}=1.4$
$\therefore$ ${\gamma }_{diatomic}<{\gamma }_{monoatomic}$

Hence, option A is correct.