Question

The heat capacity of a diatomic gas is greater than the heat capacity of a monatomic gas. Explain.

Answer 1

The heat capacity is explained by another concept called 'degrees of freedom'.

Degrees of freedom of gas molecules indicate the number of ways a given gas molecule could move in 3 spatial dimensions.
A stationary gas molecule will move when we give certain amount of energy (be it in the form of electromagnetic or thermal) to the molecule. The resulting movement can be translational (moving along the 3 axes;3 degrees of freedom), rotational (clockwise,anti-clockwise;2 degrees of freedom) or vibrational (1 degree of freedom).Thus, for mono-atomic and di-atomic gas molecules we have total possible degrees of freedom as 6. At room temperature, the monoatomic gases have only 3 degrees of freedom (an atom cannot rotate around its own; the same with vibration), whereas diatomic molecules have 5 degrees of freedom (3 translational+2 rotational).

Temperature rise in gases arise as a result of increase in the translational kinetic energy of gas molecules.

Now,suppose same amount of energy to the mono- and di-atomic gases. The mono-atomic gas will spend all energy on translation and result in temperature rise. But, the di-atomic gas will spend that energy on translational as well as rotational motion. This way, the translational component gets lesser fraction of the same energy, causing lower temperature rise compared to the mono-atomic gas. So,to have same temperature rise, we need to give the di-atomic gas more energy. In other words,heat capacity of a diatomic gas is greater than the heat capacity of a monatomic gas.