Verified Solution • 2025–26 Session moderate

QJEEM19Ph4508: JEE Main 2019 Physics - Class 11 JEEM19Ph4508 Solution: The specific heats, C P and C V of a gas of diatomic molecules, …

The specific heats, CP and CV of a gas of diatomic molecules, A, are given (in units of J mol–1 K–1) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-

Multiple Choice Options

  • A A is rigid but B has a vibrational mode
  • B A has a vibrational mode but B has none
  • C A has one vibrational mode and B has two
  • D Both A and B have a vibrational mode each

Step-by-Step Verified Solution

For A:
CpCv=γ=1+2f=2922{{{C_p}} \over {{C_v}}} = \gamma = 1 + {2 \over f} = {{29} \over {22}}
It gives f = 6.3 ≈\approx 6 (3 translational, 2 rotational and 1 vibrational)

For B:
CpCv=γ=1+2f=3021{{{C_p}} \over {{C_v}}} = \gamma = 1 + {2 \over f} = {{30} \over {21}}
∴\therefore f = 4.67 ≈\approx 5 (3 translational, 2 rotational, no vibrational)

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