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Cₚ and C_v are specific heats at constant pressure and volume respectively. It is observed that Cₚ − C_v = a for hydrogen gas Cₚ − C_v = b for nitrogen gas The correct relation between a and b is:

1. a = 14 b
2. a = 28 b
3. a = −1/14 b
4. a = b

Correct answer: a = 14 b

Solution

The specific heat difference for ideal gases is related to the degrees of freedom of the gas molecules. Hydrogen, being a diatomic gas with more vibrational modes, has a larger difference between its specific heats compared to nitrogen, leading to the relation a = 14b.

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