Question

A gas bottle contains 7.54×10²³ Oxygen molecules at a temperature of 360.0 K. What is the thermal energy of the gas? (You might need to know Boltzmann's constant: k_B = 1.38×10^-23 J/K.) How much energy is stored in ONE degree of freedom for the whole system? What is the average energy of a single molecule? On average how much energy is stored by ONE degree of freedom for ONE single molecule?

Answer 1

By kinetic theory of gases, the internal energy of a diatomic gas is given by

Substituting values

There are five degrees of freedom for a diatomic molecule. The three translational degrees of freedom and two rotational degrees of freedom. Energy stored in 1 degree of freedom for the whole system is

There are N=7.54×10²³ molecules in the gas. The average energy of a single molecule is

Each molecule has five degrees of freedom. The energy stored in one degree of freedom for one single molecule is