Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

If $C_p$ and $C_v$ denote the specific heats (per unit mass) of an ideal gas of molecular weight $M$ then: (2010 Mains)
$C_p - C_v = R/M^2$
$C_p - C_v = R$
$C_p - C_v = MR$
$C_p - C_v = \frac{R}{M}$

Solution Explained:

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

Mayer's relation for molar heat capacities is $C_P - C_V = R$. Since molar heat capacity is related to specific heat capacity by $C = Mc$, we have $M C_p - M C_v = R$, which gives $C_p - C_v = \frac{R}{M}$.

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