Question 855: Thermodynamics & KTG

Question

An ideal gas expands adiabatically. $$(\gamma=1 \cdot 5)$$ To reduce the r.m.s. velocity of the molecules 3 times, the gas has to be expanded

Accepted Answer

We know,
$$\begin{aligned}
& V_{	ext {rms }}=\sqrt{\frac{3 R T}{M_0}} \
& \Rightarrow T \propto V^2 \
& \frac{T_2}{T_1}=\frac{V_2^2}{V_1^2}=\frac{\left(\frac{V_1}{3}ight)^2}{V_1^2}=\frac{1}{9} \quad 	ext{.... (i)}\
& 	ext { Also, } T V^{\gamma-1}=	ext { Constant } \
& \Rightarrow \frac{V_2}{V_1}=\left(\frac{T_1}{T_2}ight)^{\frac{1}{\gamma-1}} \
& \frac{V_2}{V_1}=(9)^2=81
\end{aligned}$$

Answer

81 times

Answer

27 times

Answer

9 times

Answer

3 times

Thermodynamics & KTG

An ideal gas expands adiabatically. $(\gamma=1 \cdot 5)$ To reduce the r.m.s. velocity of the molecules 3 times, the gas has to be expanded

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