What is kinetic interpretation of temperature?

Solution

According to the kinetic theory of gases pressure of an ideal gas is given by,

P = \frac{1}{3} {ρv}^{2} = \frac{1}{3} \frac{M}{V} v^{2}

where, v is the mean of the square speed.

\Rightarrow

PV = \frac{1}{3} {Mv}^{2}

Now, average translational kinetic energy of the molecule is given by,

\Rightarrow

\frac{1}{2} {Mv}^{2} = \frac{3}{2} PV = \frac{3}{2} nRT

\Rightarrow

\frac{1}{2} {Mv}^{2} = \frac{3}{2} nNkT

\Rightarrow

\frac{1}{2} (\frac{M}{nN}) v^{2} = \frac{3}{2} kT

\frac{1}{2} {mv}^{2} = \frac{3}{2} kT

T: absolute temperature.

This is the relation between average kinetic energy of a molecule of gas and absolute temperature of the gas.

According to this relation average kinetic energy of a molecule of an ideal gas is proportional to its absolute temperature; is indeppendent of the pressure, volume or the nature of the ideal gas. This is called kinetic interpretation of temperature.

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

What is kinetic interpretation of temperature?

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