Figure shows a parabolic graph between T and $\frac{1}{V} (T = t e m p e r a t u r e, V = V o l u m e)$ for a gas undergoing an adiabatic process. If the ratio of rms velocity of molecules and speed of sound in the gas at the same temperature is $\sqrt{n}$ , then find the value of n.

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Solution

$\frac{1}{V} = C T^{2}$
$T^{2} V = C_{1}$
$T V^{1 / 2} = C_{1}$
$T V^{1 / 2} = C_{2}$
$T V^{r - 1} = c o n s t a n t$
$r = 3 / 2$
$V_{r m s} = \sqrt{\frac{3 R T}{M}}, V_{s o u n d} = \sqrt{\frac{γ R T}{M}}$
$\frac{V_{r m s}}{V_{s o u n d}} = \sqrt{\frac{3}{r}} = \sqrt{2}$

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Figure shows a parabolic graph between T and 1V(T=temperature,V=Volume) for a gas undergoing an adiabatic process. If the ratio of rms velocity of molecules and speed of sound in the gas at the same temperature is √n, then find the value of n.

1V=CT2T2V=C1TV1/2=C1TV1/2=C2TVr−1=constantr=3/2Vrms=√3RTM,Vsound=√γRTMVrmsVsound=√3r=√2

Figure shows a parabolic graph between T and $\frac{1}{V} (T = t e m p e r a t u r e, V = V o l u m e)$ for a gas undergoing an adiabatic process. If the ratio of rms velocity of molecules and speed of sound in the gas at the same temperature is $\sqrt{n}$ , then find the value of n.

$\frac{1}{V} = C T^{2}$
$T^{2} V = C_{1}$
$T V^{1 / 2} = C_{1}$
$T V^{1 / 2} = C_{2}$
$T V^{r - 1} = c o n s t a n t$
$r = 3 / 2$
$V_{r m s} = \sqrt{\frac{3 R T}{M}}, V_{s o u n d} = \sqrt{\frac{γ R T}{M}}$
$\frac{V_{r m s}}{V_{s o u n d}} = \sqrt{\frac{3}{r}} = \sqrt{2}$