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The relation between the pressure $(\mathrm{P})$, volume $(\mathrm{V})$ and average kinetic energy (E) of a gas is
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Verified Answer
The correct answer is:
$P=\frac{2}{3} \frac{E}{V}$
Kinetic energy is given by
$\begin{aligned}
& \mathrm{K} . \mathrm{E}=\frac{3}{2} \mathrm{RT} \\
& \text { since, } \mathrm{PV}=\mathrm{n} \mathrm{RT} \\
& \text { Here } \mathrm{n}=1 \\
& \mathrm{E}=\frac{3}{2} \mathrm{PV} \Rightarrow \mathrm{P}=\frac{2 \mathrm{E}}{3 \mathrm{~V}}
\end{aligned}$
$\begin{aligned}
& \mathrm{K} . \mathrm{E}=\frac{3}{2} \mathrm{RT} \\
& \text { since, } \mathrm{PV}=\mathrm{n} \mathrm{RT} \\
& \text { Here } \mathrm{n}=1 \\
& \mathrm{E}=\frac{3}{2} \mathrm{PV} \Rightarrow \mathrm{P}=\frac{2 \mathrm{E}}{3 \mathrm{~V}}
\end{aligned}$
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