Question

One mole of an ideal monoatomic gas is mixed with 1 mole of an ideal diatomic gas. The molar-specific heat of the mixture at constant volume is:

• A. $3\mathrm{cal}$
• B. $4\mathrm{cal}$
• C. $8\mathrm{cal}$
• D. $9\mathrm{cal}$

Answer 1

The correct option is B

$4\mathrm{cal}$

Explanation for Correct answer:

Option B $4\mathrm{cal}$

Step 1 Molar-specific heat

For monoatomic, the molar-specific heat of constant volume ${\mathrm{C}}_{\mathrm{v}}=\frac{3}{2}\mathrm{R}$

For diatomic, the molar-specific heat of constant volume ${\mathrm{C}}_{\mathrm{v}}=\frac{5}{2}\mathrm{R}$

For mixture, the molar-specific heat of constant volume will be the average of both,

$$\begin{gathered} {\mathrm{C}}_{\mathrm{v}}=\frac{\frac{3}{2}\mathrm{R}+\frac{5}{2}\mathrm{R}}{2} \\ {\mathrm{C}}_{\mathrm{v}}=\frac{\frac{8}{2}\mathrm{R}}{2} \\ {\mathrm{C}}_{\mathrm{v}}=\frac{4\mathrm{R}}{2} \\ {\mathrm{C}}_{\mathrm{v}}=2\mathrm{R} \end{gathered}$$

Therefore, the molar-specific heat of the mixture at constant volume is $4\mathrm{cal}$ that is, the option (B) is correct.