Question

A gas mixture consist of 3.0 mole of hydrogen and 2.0 mole of helium at absolute temperature T considering all vibrational modes the total internal energy of system is

Answer 1

hydrogen is diatomic gas , so molar specific heat capacity at constant volume, $C_1=\frac{5R}{2}$

number of mole of hydrogen, $n_1$ = 3

helium is monoatomic gas, so molar specific heat capacity at constant volume, $C_2=\frac{3R}{2}$

number of mole of helium, $n_2$ = 2.

now, internal energy of system = $n_1C_1T+n_2C_2T$

= 3 × 5R/2 × T + 2 × 3R/2 × T

= 21RT/2

= (10.5)RT