JEE Main & Advanced Sample Paper JEE Main - Mock Test - 4

Figure shows a parabolic graph between T and 1/V for a mixture of a gas undergoing an adiabatic process. What is the ratio of \[{{V}_{rms}}\] of molecules and to speed of sound in mixture?

A) \[\sqrt{3/2}\]

B) \[\sqrt{2}\]

C) \[\sqrt{2/3}\]

D) \[\sqrt{3}\]

Correct Answer: B

Solution :

From graph, \[{{T}^{2}}V\]= const.	.....(1)
As we know that \[T{{V}^{\gamma -1}}=\] const.
\[\Rightarrow \,\,\,\,V{{T}^{\frac{1}{\gamma -1}}}=\] cons.	....(2)
On comparing (1) and (2), we get
\[\Rightarrow \,\,\,\gamma =3/2\]
Also \[{{\text{v}}_{rms}}=\sqrt{\frac{3P}{\rho }}\] and \[{{\text{v}}_{sound}}=\sqrt{\frac{P\gamma }{\rho }}\]
\[\Rightarrow \,\,\,\frac{{{\text{v}}_{rms}}}{{{\text{v}}_{sound}}}=\sqrt{\frac{3}{\gamma }}=\sqrt{2}\]