Question

For a gas of non rigid mono-atomic molecules, the value of heat capacity ratio γ is:
1. \(\dfrac{7}{5}\)
2. \(\dfrac{5}{3}\)
3. \(\dfrac{9}{7}\)
4. \(\dfrac{11}{9}\)

Answer 1

Correct Answer - Option 2 : \(\dfrac{5}{3}\)

CONCEPT:

Molecular specific heat at constant volume Cv = fR/2

molecular specific heat at constant pressure Cp = Cv + R = (2 + f)R/2

where f is the degree of freedom.

• Degree of Freedom (DOF): 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 monoatomic molecule, so f = 3

Cv = fR/2 = 3R/2

Cp = (2 + f)R/2 = 5R/2

\(\gamma = \dfrac{C_P}{C_V}=\dfrac{5}{3}\)

So the correct answer is option 2.