Question

What is \( C_v \) for a monoatomic gas?

Hint:

For a monoatomic ideal gas, \( C_v = \frac{3}{2} R \), which is derived from the translational degrees of freedom.

Answer 1

Step 1: Understanding the heat capacities.
For a monoatomic ideal gas, the heat capacity at constant volume \( C_v \) is related to the ideal gas constant \( R \). In the case of a monoatomic gas, the degrees of freedom are three translational degrees of freedom, and the heat capacity is derived using the equipartition theorem.
Step 2: Formula for \( C_v \).
For a monoatomic ideal gas, the formula for \( C_v \) is: \[ C_v = \frac{3}{2} R \] where \( R \) is the universal gas constant.
Step 3: Conclusion.
Thus, the heat capacity at constant volume for a monoatomic gas is \( \frac{3}{2} R \).