Question

In a certain gas, the ratio of the speed of sound and root mean square speed is $\frac{5}{9}$. The molar heat capacity of the gas in a process given by PT = constant is
(Take R = 2 cal/mole K). Treat the gas as ideal.

• A. $\frac{f+2}{f}$
• B. $\frac{3R}{2}$
• C. $\frac{5R}{2}$
• D. $\frac{7R}{2}$

Answer 1

The correct option is A $\frac{f+2}{f}$

$\begin{array}{c}{V}_{sound}=\sqrt{\frac{\gamma RT}{M}}\\ V_{rms}=\sqrt{\frac{3RT}{M}}\\ \Rightarrow \sqrt{\frac{\gamma }{3}}=\frac{5}{9}\\ \Rightarrow \frac{\gamma }{3}=\frac{25}{81}\\ \Rightarrow \gamma =\frac{25}{27}=\frac{f+2}{f}\end{array}$

Hence,

Option $A$ is correct answer.