Question

Internal energy and pressure of a gas per unit volume are related as

• A. $p=\frac{2}{3}E$
• B. $p=\frac{3}{2}E$
• C. $p=\frac{1}{2}E$
• D. p = 2E

Answer 1

Answer: (A)

$p=\frac{2}{3}E$

Answer 2

The average translational kinetic energy of a gas
molecule is $\frac{1}{2}$ $m \overline{u}^2\, \, \, \, \, \, \, \, \, ...(i)$
The total energy of the whole of the gas containing
N molecules is
$E_k=\frac{1}{2}m N \overline{u}^2\, \, \, \, \, \, \, \, \, ...(i)$
The kinetic gas equation is
$pV=\frac{1}{3}m N \overline{u}^2\, \, \, \, \, \, \, \, \, ...(ii)$
$pV=\frac{2}{3}\times\frac{1}{2}m N \overline{u}^2$
$pV=\frac{2}{3} E_k\, \, \, \, \, \, \, \, \, \, \, \, \, \, ...(iii)$
so, $\, \, \, \, \, \, \, \, \, \, \, \, p=\frac{2}{3} E_k$per unit volume