Question

Equal volumes of two monoatomic gases, A and B, at same temperature and pressure are mixed. The ratio of specific heats $(C_p/C_v)$ of the mixture will be -

• A. 1.5
• B. 3.3
• C. 1.67
• D. 0.83

Answer 1

The Correct Option is C

To determine the ratio of specific heats $(C_p/C_v)$ for the mixture of two monoatomic gases A and B at the same temperature and pressure, we begin by recalling some important concepts regarding specific heats:

For a monoatomic gas, the degrees of freedom (f) is 3. The specific heat capacities at constant pressure (C_p) and at constant volume (C_v) can be expressed as:

• C_v = \frac{f}{2}R = \frac{3}{2}R
• C_p = C_v + R = \frac{3}{2}R + R = \frac{5}{2}R

The ratio of specific heats, also known as the adiabatic index (\gamma), is given by:

• \gamma = \frac{C_p}{C_v} = \frac{\frac{5}{2}R}{\frac{3}{2}R} = \frac{5}{3} \approx 1.67

Since both gases A and B are monoatomic and mixed in equal volumes, the mixture behaves similarly to the individual gases. Therefore, the ratio of specific heats for the mixture remains:

• \gamma_{mixture} = 1.67

Thus, the correct answer is: 1.67