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MHT CET Medical202621 April 2026Evening ShiftPhysicsKinetic Theory of GasesActual

If a non-linear polyatomic gas has f vibrational nodes, the value of = C_p/C_v is ( C_p and C_v are specific heats at constant pressure and volume respectively)

Options

  1. A4+f 2+f
  2. B3+f 4-f
  3. Cf-4 3+f
  4. D4+f 3+f

Correct answer

D. 4+f 3+f

Step-by-step solution

For a non-linear polyatomic gas, the number of translational degrees of freedom is 3 and the number of rotational degrees of freedom is 3 . Each vibrational mode contributes 2 degrees of freedom, one associated with kinetic energy and the other with potential energy. Therefore, f vibrational modes contribute 2f degrees of freedom. The total number of degrees of freedom N is: N = 3 + 3 + 2f = 6 + 2f The molar specific heat at constant volume C_v is given by N 2 R . C_v = 6 + 2f 2 R = (3 + f)R Using Mayer's relation,

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