Oxygen (O 2 ) is confined to a cubic container, 15 cm on a side, at a temperature of 300 K. Compare the average kinetic energy of a molecule of the gas to the change in its gravitational potential energy if it falls from the top of the container to the bottom.

Average kinetic energy is greater than gravitational potential energy.

Explanation: The average kinetic energy formulae for a molecule of a gas relative to temperature (in Kelvin) is given below as

E = 3/2 (KT).

Where E = average kinetic energy =?

K = boltzman constant = 1.381×10^-23 m²kg/s²k

T = temperature = 300 k

By substituting the parameters in the formulae, we have that

E = 3/2 ×( 1.381×10^-23 × 300)

E = 1.5 × 4.143×10^-21

E = 6.2145×10^-21 J

To get the gravitational potential energy, we use the fact that

Gravitational potential energy = gravitational energy at the top - gravitational energy at bottom.

At the top, the height of cube is h= 15cm = 0.15m, g = acceleration dude to gravity = 9.8m/s², m = mass of molecule of oxygen = 1.661×10^-27 kg

Gravitational potential energy = mgh = 1.661×10^-27× 9.8 × 0.15 = 2.442×10^-27 J

At the bottom, height is zero, hence gravitational potential energy is also zero.

Hence the final gravitational potential energy = potential energy at top - potential energy at bottom =

2.442×10^-27 - 0 = 2.442×10^-27 J.

Gravitational potential energy = 2.442×10^-27 J

Average kinetic energy = 6.2145×10^-21 J

As we can see that the average kinetic energy is bigger than the gravitational potential energy.