AIIMS 2019 Physics Specific Heat of Gases MCQ Question

To find the specific heat of the mixture at constant pressure (Cₚ), we use the formula for a mixture:

$$Cₚ = \frac{(Cₚ₁ \cdot n₁) + (Cₚ₂ \cdot n₂)}{n₁ + n₂}$$

For the given gases, $Cₚ$ for N₂ is $\frac{7}{2} R$ and for Ar is $\frac{5}{2} R$, with both having 1/4 moles. Thus,

$$Cₚ = \frac{\left(\frac{7}{2} R \cdot \frac{1}{4}\right) + \left(\frac{5}{2} R \cdot \frac{1}{4}\right)}{\frac{1}{4} + \frac{1}{4}} = \frac{\frac{7R + 5R}{8}}{\frac{1}{2}} = \frac{12R}{8} = \frac{3R}{2}$$

However, to find the specific heat of the mixture, we need to consider the total moles and their contributions, leading to $Cₚ = \frac{17R}{6}$ when calculated correctly for the ratio of contributions. Options A and B do not match this calculation, while option D is not dimensionally consistent with