The calculation of thermal energy for diatomic gases is represented by the formula (5/2)PV, where 5/2 is derived from the degrees of freedom of the gas molecules. Diatomic gases have 7 total degrees of freedom (3 translational, 2 rotational, and 2 vibrational), but typically only 5 are counted due to the vibrational modes being "frozen out." For monatomic gases, the ratio is (3/2)PV. The specific heat capacity at constant volume (CV) for diatomic gases is thus 5/2R per mole, while for monatomic gases it is 3/2R per mole. The heat capacity ratio, γ, is defined as CP/CV, where CP is the specific heat capacity at constant pressure.
PREREQUISITESStudents in thermodynamics courses, physics enthusiasts, and professionals in engineering fields focusing on gas behavior and thermal energy calculations.
K^2 said:This is value known as specific heat capacity at constant volume, or CV. You obtain said quantity by counting degrees of freedom and dividing it by 2. For diatomic gas, there are 7 total, 3 translational, 2 vibrational, and 2 rotational, but the 2 vibrational degrees of freedom are typically "frozen out". So you only count the 5. That gives you the 5/2. For monatomic gas, there are only the translational, so you get 3/2.
Realistically, the value will be off by a bit. There is an associated quantity γ=CP/CV known as heat capacity ratio. You can look it up for gas of interest, and use the fact that CP=CV+1 to compute the actual ratio.
Note that all these values are in units of R. So the actual specific heat capacity of diatomic gas at constant volume will be 5/2R per mole of gas.