First slide

Calculation of pressure

Question

The pressure of an ideal gas is directly proportional to [UK PMT 2015]

Moderate

A

total kinetic energy
B

translational kinetic energy
C

rotational kinetic energy
D

vibrational kinetic energy

Solution

Translational kinetic energy,
$K = \frac{1}{2} M v_{r m s}^{2}$ …(i)
and $v_{rms} = \sqrt{\frac{3 p V}{M}}$ …(ii)
From Eqs. (i) and (ii), we get
$K = \frac{1}{2} M \frac{3 p V}{M} = \frac{3}{2} p V$
$\Rightarrow$ $p = \frac{2 K}{3 V} \Rightarrow p \propto K$ (If, V = constant)

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