Question

Find the total translational kinetic energy of 0.5 L of oxygen gas held at a temperature of −6 ◦C and a pressure of 2 atm. Answer in units of J.

Answer 1

At temperature T, the average energy of each degree of freedom of a molecule of a gas is kT/2. In translational motion, there are 3 degrees of freedom. The average translational energy of a single molecule of the gas is

$K_1=\frac12kT+\frac12kT+\frac12kT$

$K_1=\frac32kT$

Let there be N molecules in the gas, the total translational energy of the gas is

K=NK = NKT

Using ideal gas equation PV=NKT we get

312

Substituting we get

P=2 atm = 2 x 1.01 x 105 Pa, V = 0.5 L = 0.5 x 10-3 m3

K= 2x (2 x 1.01 x 105 Pa) x (0.5 x 10-3 m3)

K = 151.5 J