Question

What is the ratio \( \frac{C_p}{C_v} \) for a monatomic and diatomic gas?

Hint:

The value of \( \gamma = \frac{C_p}{C_v} \) depends on the number of degrees of freedom of the gas molecules. For monatomic gases, it is higher than for diatomic gases.

Answer 1

The ratio of specific heats \( \frac{C_p}{C_v} \) for an ideal gas is given by: \[ \gamma = \frac{C_p}{C_v}. \] For a monatomic ideal gas, the value of \( \gamma \) is \( \frac{5}{3} \), because a monatomic gas has only translational degrees of freedom. For a diatomic ideal gas, the value of \( \gamma \) is \( \frac{7}{5} \), because a diatomic gas has translational and rotational degrees of freedom. At high temperatures, it may also have vibrational degrees of freedom, but in this case, we're assuming it to be a simple diatomic molecule. Thus, \( \frac{C_p}{C_v} = \frac{3}{2} \) for monatomic and \( \frac{C_p}{C_v} = \frac{5}{3} \) for diatomic.