First slide

Kinetic theory of ideal gases

Question

The total kinetic energy of translatory motion of all the molecules of 5 litres of nitrogen exerting a pressure P is 3000 J.

Moderate

A

The total k.E. of 10 litres of N₂ at a pressure of 2P is 3000J
B

The total k.E. of 10 litres of He at a pressure of 2P is 3000J
C

The total k.E. of 10 litres of O₂ at a pressure of 2P is 20000J
D

The total k.E. of 10 litres of Ne at a pressure of 2P is 15000 J

Solution

K.E of translation of any gas = $\frac{3}{2} n R T = \frac{3}{2} P V$
Given, $3000 = \frac{3}{2} P V \Rightarrow P V = 2000$ (1)
Total KE of a gas = $\frac{f}{2} n R T = \frac{f}{2} P V$
f = 5 (for N₂ and O₂ ) f = 3 (for He and Ne).
Hence, for $O_{2} a n d N_{2}$ , $E = \frac{5}{2} (2 P) (2 V) = (10) P V = 10 (2000) = 20000 J$
And for He and Ne, $E = \frac{3}{2} (2 P) (2 V) = 6 P V = 6 (2000) = 12000 J$ .

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