Question

What is the relationship between the temperature of a gas and its distribution of kinetic energies? Is it possible to have particles with kinetic energies many multiples of the most common value? What is the relationship between the speed distribution of a gas and the mass of the particles? How does this help to explain the relative ease with which hydrogen escapes from its containers?

Answer 1

(a) What is the relationship between the temperature of a gas and its distribution of kinetic energies?

using an ideal gas law, we have

P V = n R T

An expression for gas pressure developed from kinetic theory which relates pressure & volume to the average molecular kinetic energy.

P V = (2/3) N [(1/2) m v²]

equating above two eq. & we get -

(2/3) N [(1/2) m v²] = n R T

T = (2/3) (N / n R) [(1/2) m v²]

where, N = number of molecules

n = number of moles

R = gas constant

k = boltzmann constant

T = (2/3) (1/k) [(1/2) m v²]

K.E = (3/2) k T

(b) Yes, it is possible to have particles with kinetic energies have many multiples of the most common value.

(c) What is the relationship between the speed distribution of a gas and the mass of the particles?

v_rms = 3 k T / m

where, m = mass of the particle

T = temperature of a gas