Question 812: Thermodynamics & KTG

Question

In a vessel, the ideal gas is at a pressure $\mathrm{P}$. If the mass of all the molecules is halved and their speed is doubled, then resultant pressure of the gas will be

Accepted Answer

We know,
$\begin{aligned}
& \mathrm{v}_{\mathrm{ms}}^2=\frac{3 \mathrm{PV}}{\mathrm{Nm}} \
& \Rightarrow \mathrm{P}=\frac{1}{3} \frac{\mathrm{mN}}{\mathrm{V}} \mathrm{v}_{\mathrm{mms}}^2 \
& \Rightarrow \mathrm{P} \propto \mathrm{v}_{\mathrm{ms}}^2 \
& 	herefore \quad \frac{\mathrm{P}_2}{\mathrm{P}_1}=\frac{\mathrm{m}_2}{\mathrm{~m}_1} 	imes\left[\frac{\mathrm{v}_2}{\mathrm{v}_1}ight]^2 \
&=\frac{\left(\frac{\mathrm{m}_1}{2}ight)}{\mathrm{m}_1}\left[\frac{2 \mathrm{v}_1}{\mathrm{v}_1}ight]^2 \
& \ldots . .\left(\because 	ext { given } \mathrm{m}_2=\frac{\mathrm{m}_1}{2} 	ext { and } \mathrm{v}_2=2 \mathrm{v}_1ight)
\end{aligned}$
$\begin{aligned}
\frac{\mathrm{P}_2}{\mathrm{P}_1} & =2 \
	herefore \quad \mathrm{P}_2 & =2 \mathrm{P}_1 \
& =2 \mathrm{P} \quad .... (	ext{given} ~\mathrm{P_1=P})
\end{aligned}$

Answer

$4 \mathrm{P}$

Answer

$2 \mathrm{P}$

Answer

$\mathrm{P}$

Answer

$\frac{\mathrm{P}}{2}$

Thermodynamics & KTG

In a vessel, the ideal gas is at a pressure \mathrm{P}. If the mass of all the molecules is halved and their speed is doubled, then resultant pressure of the gas will be

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