Question

a cylinder of oxygen gas is cooled from 300K to 150K by what factor does the average kinetic energy of the oxygen molecules in the cylinder decrease

Answer 1

Temperature is a measure of average kinetic energy thus absolute temperature is proportional to average kinetic energy. It should be half: same factor as the temperature.

Answer 2

Answer:

The factor by which the average kinetic energy of the oxygen molecules in the cylinder decreases is '0.5'.

Explanation:

Average kinetic energy is defined as the average of the kinetic energies of all the particles present in a system. It is determined by the equation:

$K=\frac{3RT}{2N_A}$

where,

K = Average kinetic energy

R = Gas constant

T = Temperature of the system

$N_A$ = Avogadro's number

Average kinetic energy of oxygen gas molecule at 300 K.

$K.E=\frac{3R\times 300 K}{2N_A}$..[1]

Average kinetic energy of oxygen gas molecule at 150 K.

$K.E'=\frac{3R\times 150 K}{2N_A}$..[2]

[1] ÷ [2]

$\frac{K.E}{K.E'}=\frac{\frac{3R\times 300 K}{2N_A}}{\frac{3R\times 150 K}{2N_A}}=\frac{300}{150}=2$

$K.E'=0.5\times K.E$

The factor by which the average kinetic energy of the oxygen molecules in the cylinder decreases is '0.5'.