Question

For a gas of non rigid diatomic molecules, the value of \(\gamma = \dfrac{C_P}{C_V}\) is:
1. \(\dfrac{9}{7}\)
2. \(\dfrac{7}{5}\)
3. \(\dfrac{5}{3}\)
4. \(\dfrac{11}{9}\)

Answer 1

Correct Answer - Option 2 : \(\dfrac{7}{5}\)

CONCEPT:

Molecular specific heat at constant volume C_v = fR/2

molecular specific heat at constant volume Cp = C_v + R = (2 + f)R/2

where f is the degree of freedom.

• Degree of Freedom: The number of independent ways by which a gas molecule can move, without any constraint imposed on it, is called the number of degrees of freedom.
  • For monoatomic molecule f = 3.
  • For diatomic molecule f = 5

CALCULATION:

Given that diatomic molecule, so f = 5

Cv = fR/2 = 5R/2

Cp = (2 + f)R/2 = 7R/2

\(\gamma = \dfrac{C_P}{C_V}=\dfrac{7}{5}\)

So the correct answer is option 2.