Question

Show that pressure of gas is equal to two-third of kinetic energy per unit volume of gas.

Solution

Pressure of a gas is given by P =

\frac{1}{3} ρ v^{2}

... (1)
Density is equal to mass per unit volume.
Density,

ρ

\frac{M}{V}

Now, multiplying and dividing equation (1) by 2, we get

P = \frac{2}{3} \frac{1}{V} (\frac{1}{2} {Mv}^{2}) = \frac{2}{3 V} (Kinetic energy of gas) = \frac{2}{3} (\frac{Kinetic energy of gas}{Volume}) P = \frac{2}{3} (K . E per unit volume of gas)

Hence proved.

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