Question

how specific heat capacity of monoatomic and diatomic gases can be explained on the equi -partition of energy​

Answer 1

Answer:

Explanation:

From law of equipartition of energy, energy per each degree of freedom is 12kBT per atom or molecule.

1. Monoatomic gas has three degrees of freedom.

∴U1=3×12KB.TordUdT=32KB.T

But molar specific heat at constant volume CV=dUdT

∴CV=32KBTNA,ButKBNA=R

∴CV=32RT,ButCP=CV+R∴CP=52R

(2) A diatomic gas has 3 translational and two rational degrees of freedom

∴ Kinetic energy per molecule

U1=5.12KB.T

For one gram mole total energy

U=52KB.T.NA

Molar specific heat at constant volume

CV=dUdT=52KB.NA

∴CV=52R&CP=52R+R=72R

(3) A polyatomic gas has three translational three ratitional and at least one vibrational degrees of freedom.

∴ Kinetic energy per molecule

U1=3.12KB.T+3.12+f=(3+f)KBT

f = Number of vibrational degree of freedom

kinetic energy

= per gram mole of molecules

=U1NA=U=(3+f)KB.NA.T=(3+f)RT

Molar specific heat CV=dUdT=(3+f)R

∴CP=(u+f)R

∴ For polyatomic gases CV=(3+f)R&CP=(4+f)R.