C_p/C_v for monoatomic gas is 1.67 , for diatomic gas is 1.41 , for tri atomic gas is 1.33

What is C_p/C_v when mixed following:-

1. mono & diatomic

2. Diatomic & triatomic

3. triatomic & monoatomic

To determine the ratio of specific heats, C_p/C_v, for mixtures of gases, we can use the concept of weighted averages based on the molar fractions of each gas in the mixture. The specific heat capacities for the gases you mentioned are as follows: for monoatomic gases, C_p/C_v is 1.67; for diatomic gases, it is 1.41; and for triatomic gases, it is 1.33. Let's break down the calculations for each mixture step by step.

1. Mixture of Monoatomic and Diatomic Gases

Let's assume we have a mixture of one mole of monoatomic gas and one mole of diatomic gas. The total number of moles in the mixture is 2. The molar fractions are:

• Monoatomic gas: X_mono = 1/2
• Diatomic gas: X_diatomic = 1/2

Now, we can calculate the C_p/C_v for the mixture:

C_p/C_v = X_mono * (C_p/C_v)_mono + X_diatomic * (C_p/C_v)_diatomic

Substituting the values:

C_p/C_v = (1/2) * 1.67 + (1/2) * 1.41 = 0.835 + 0.705 = 1.54

2. Mixture of Diatomic and Triatomic Gases

For a mixture of one mole of diatomic gas and one mole of triatomic gas, the total number of moles remains 2, with the following molar fractions:

• Diatomic gas: X_diatomic = 1/2
• Trioatomic gas: X_triatomic = 1/2

Now, we calculate the C_p/C_v for this mixture:

C_p/C_v = X_diatomic * (C_p/C_v)_diatomic + X_triatomic * (C_p/C_v)_triatomic

Substituting the values:

C_p/C_v = (1/2) * 1.41 + (1/2) * 1.33 = 0.705 + 0.665 = 1.37

3. Mixture of Triatomic and Monoatomic Gases

For a mixture of one mole of triatomic gas and one mole of monoatomic gas, the total number of moles is again 2, with the following molar fractions:

• Trioatomic gas: X_triatomic = 1/2
• Monoatomic gas: X_mono = 1/2

Now, we calculate the C_p/C_v for this mixture:

C_p/C_v = X_triatomic * (C_p/C_v)_triatomic + X_mono * (C_p/C_v)_mono

Substituting the values:

C_p/C_v = (1/2) * 1.33 + (1/2) * 1.67 = 0.665 + 0.835 = 1.50

Summary of Results

• Monoatomic & Diatomic: C_p/C_v = 1.54
• Diatomic & Triatomic: C_p/C_v = 1.37
• Trioatomic & Monoatomic: C_p/C_v = 1.50

This method of calculating the specific heat ratio for mixtures is quite useful in thermodynamics, especially when dealing with real-world gas mixtures in various applications. If you have any further questions about this topic or related concepts, feel free to ask!