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Asked by Manish Last Modified
Answer 
Here is the proof for the question
| According to the kinetic equation of pressure of a gas:
P = r 1/3 | |
| But r = density of gas | |
| P = 1/3 (mN / V ) | |
| But PV = nRT | |
| nRT= 1/3 (mN) | |
| Since | |
| Therefore, | |
| [N/NA] R T= 1/3 (mN) | |
| But NA R = Boltzman’s constant (K), thus, | |
| 3 K T= (m) | |
| Multiplying both sides by 1/2 | |
| (3/2) K T= (1/2) m | |
| (1/2) m = (3/2) K T | |
| But (1/2) m = average translational kinetic energy of gas molecules = (K.E)av | |
| (K.E)av = (3/2) K T | |
| As (3/2) K is a constant term, therefore, | |
| (K.E)av = (constant) T
| |
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