Question

The pressure P of an ideal gas and its mean kinetic energy E per unit volume are related as:

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

Answer 1

The correct option is D $P$ = $\frac{2E}{3}$

The mean kinetic energy of a gas per mole is $E=\frac{3}{2}nRT$ _____ (1)

The pressure of an ideal gas is given by: $PV=nRT$

i.e per unit volume 'P'

$P=nRT$

By putting the value of $P$ in the above equation-1

we get, $P=\frac{2}{3}E$

Hence, option $D$ is correct.