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Q.
Internal energy and pressure of a gas per unit volume are related as
AIPMTAIPMT 1993States of Matter
Solution:
According to the kinetic gas equation, $pV =\frac{1}{3} mnc ^{2}$
$=\frac{1}{3} Mc ^{2} \,\,\,\, ( M = mn )$
$=\frac{2}{3} \times \frac{1}{2} Mc ^{2} $
$=\frac{2}{3} E _{ K } \,\,\,\,\left( E _{ K }=\frac{1}{2} Mc ^{2}\right)$
Dividing both sides by volume (V), we get
$p =\frac{2}{3} E \,\,\,\,\left( E = E _{ K } / V \right)$
Note that the internal energy of an ideal gas is equal to its kinetic energy because the potential energy of an ideal gas is zero as there is no intermolecular interaction between gas particles.