Molar Heat Capacity of Monoatomic Gas – Rankers Physics

Thermodynamics: Practice Problem & Solution

Assertion (A): Molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all temperatures. Reason (R): As the temperature of an monoatomic ideal gas is increased, number of degrees of freedom of gas molecules remains constant.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Thermodynamics. Understanding the underlying formula is key to arriving at the correct answer below:

For an ideal monoatomic gas, \(C_v = \frac{3}{2}R\) as it only has 3 translational degrees of freedom. This number \(f=3\) remains constant with temperature. Thus, \(C_v\) is constant. Reason (R) correctly explains Assertion (A).

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