NEETPhysicsKinetic Theory of Gases
Consider a linear polyatomic gas having f active vibrational modes. If is the ratio of specific heat capacities ( C_p C_v ) for this gas, the correct expression for the number of vibrational modes f in terms of is:
Options
- A4 - 3 - 1
- B7 - 5 2( - 1)
- C7 - 5 - 1
- D5 - 3 2( - 1)
Correct answer
B. 7 - 5 2( - 1)
Step-by-step solution
For a linear polyatomic gas, there are 3 translational degrees of freedom and 2 rotational degrees of freedom. Let the number of active vibrational modes be f . Each vibrational mode contributes R to the molar heat capacity at constant volume ( C_v ). The total C_v is given by: C_v = 3 2 R + 2 2 R + fR = 5 2 R + fR = ( 5 + 2f 2 )R The molar heat capacity at constant pressure ( C_p ) is: C_p = C_v + R = ( 5 + 2f 2 )R + R = ( 7 + 2f 2 )R The ratio of specific heats is: = C_p C_v = 7 + 2f 5 + 2f Rearranging to solve f