Identifying the gas

Problem

$c_V = 28{,}1\ \text{J/(K·mol)}$ and $c_p = 36{,}4\ \text{J/(K·mol)}$ are measured for a certain gas. Calculate $\gamma$ and state what type of gas it is.

Solution

Ratio of specific heats. By definition:

$\gamma=\frac{c_p}{c_V}=\frac{36{,}4}{28{,}1}=1{,}295$

Check with Mayer’s relation. For an ideal gas $c_p - c_V = R$ must hold:

$c_p - c_V = 36{,}4 - 28{,}1 = 8{,}3\approx R$

consistent with $R = 8{,}31\ \text{J/(K·mol)}$: the gas behaves ideally.

Interpretation. A value $\gamma\approx 1{,}30$ indicates many active quadratic degrees of freedom (translational, rotational and possibly vibrational). This is typical of a TRIATOMIC gas, such as CO₂ or water vapour H₂O.

$\ev{\gamma\approx 1{,}30;\ \text{triatomic gas (CO}_2,\ \text{H}_2\text{O vapour)}}$

Links

Topics: Thermodynamics Concepts: Specific heat and heat capacity · Thermodynamic processes Objects: Ideal gas