Question
An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and f number of vibrational modes. If the ratio of heat capacities C_P/C_V of the gas is 8/7, then the value of f is :
NEET
Physics
Kinetic Theory of Gases
2026
NEET 2026 (Re-NEET)
NEET Physics Question (2026) — Solution
Options
- A. 1
- B. 4
- C. 3
- D. 2
Answer
B. 4
Step-by-step solution
The internal energy of one mole of the polyatomic gas is given by the equipartition theorem. Each translational and rotational degree of freedom contributes 1 2 RT to the internal energy, while each vibrational mode contributes RT (since it has both kinetic and potential energy components). U = 3 ( 1 2 RT ) + 3 ( 1 2 RT ) + f(RT) = (3+f)RT The molar heat capacity at constant volume is: C_V = dU dT = (3+f)R The molar heat capacity at constant pressure is: C_P = C_V + R = (4+f)R The ratio of heat capacities is given as 8 7 : C_P C_V = 4+f 3+f = 8 7 28 + 7f = 24 + 8f f = 4 Answer: 4
Related: Physics — Kinetic Theory of Gases · All PYQ Banks