Q158 / 200 · MHT CET - Medical 2026 (22 April Shift 2) · Physics
The total internal energy of one mole of HCl molecule is (assume the molecule to be non-rigid)
- A$\dfrac{3}{2}RT$
- Correct answerB$\dfrac{7}{2}RT$
- C$\dfrac{5}{2}RT$
- D$\dfrac{9}{2}RT$
Solution
HCl is a diatomic molecule.
For a non-rigid diatomic molecule, the degrees of freedom are:
Translational degrees of freedom = $3$
Rotational degrees of freedom = $2$
Vibrational degrees of freedom = $2$ (since each vibrational mode contributes two degrees of freedom, one for kinetic energy and one for potential energy).
Total degrees of freedom $f = 3 + 2 + 2 = 7$.
By the law of equipartition of energy, the internal energy of one mole of a gas is given by $U = \dfrac{f}{2}RT$.
Substituting $f = 7$, we get $U = \dfrac{7}{2}RT$.
Answer: $\dfrac{7}{2}RT$
For a non-rigid diatomic molecule, the degrees of freedom are:
Translational degrees of freedom = $3$
Rotational degrees of freedom = $2$
Vibrational degrees of freedom = $2$ (since each vibrational mode contributes two degrees of freedom, one for kinetic energy and one for potential energy).
Total degrees of freedom $f = 3 + 2 + 2 = 7$.
By the law of equipartition of energy, the internal energy of one mole of a gas is given by $U = \dfrac{f}{2}RT$.
Substituting $f = 7$, we get $U = \dfrac{7}{2}RT$.
Answer: $\dfrac{7}{2}RT$
Hence, the correct answer is option: 'B'.