The values of γ = Cₚ/Cᵥ for hydrogen, helium and another ideal diatomic X (whose molecules are not rigid and have an additional vibration mode), respectively, are equal to:
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The values of γ = Cₚ/Cᵥ for hydrogen, helium and another ideal diatomic X (whose molecules are not rigid and have an additional vibration mode), respectively, are equal to:

G1 Physics · Accepted Answer

Step 1: For an ideal gas with f active energy degrees of freedom, γ = 1 + 2/f. Step 2: Hydrogen H₂ (ordinary diatomic, vibration inactive) has f = 5; γ = 1 + 2/5 = 7/5. Step 3: Helium (monoatomic) has f = 3; γ = 1 + 2/3 = 5/3. Step 4: Diatomic X with one active vibrational mode has f = 3 translational + 2 rotational + 2 vibrational = 7. Hence γ = 1 + 2/7 = 9/7. Final answer: (A) 7/5, 5/3, 9/7.