First slide

Kinetic theory of ideal gases

Question

One kilogram of a diatomic gas is at a pressure of $8 \times 10^{4} N m^{- 2}$ . The density of the gas is $4 k g m^{- 3}$ . What is the energy of the gas due to its thermal motion?

Moderate

A

$3 \times 10^{4} J$
B

$4 \times 10^{4} J$
C

$5 \times 10^{4} J$
D

$7 \times 10^{4} J$

Solution

Thermal energy corresponds to internal energy
As per law of equipartition of energy,
Energy per mole = $\frac{f R T}{2}$
Hence energy of gas = $(n u m b e r o f m o l e s) \frac{f R T}{2} = \frac{n f R T}{2} = \frac{f P V}{2}$
$= \frac{5 (8 \times 10^{4} N m^{- 2}) (\frac{1}{4} m^{3})}{2} = 5 \times 10^{4} J$

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