Thermodynamics: Practice Problem & Solution
Assertion (A): Experimental results indicate that the molar specific heat of hydrogen gas at constant volume below \( 50 \text{ K} \) is equal to \( 5/2 R \), where \( R \) is the universal gas constant. Reason (R): A diatomic hydrogen molecule possesses three translational and two rotational degrees of freedom at all temperatures.
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Thermodynamics. Understanding the underlying formula is key to arriving at the correct answer below:
Assertion (A) is false. Below \( 50 \text{ K} \), hydrogen's rotational modes freeze out, so \( C_V \) approaches \( 3/2 R \), not \( 5/2 R \).
Reason (R) is false because degrees of freedom depend on temperature; vibrational modes activate at high T, and rotational modes freeze out at low T.
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