Statistical Thermodynamics

[mccals02]

(1) Derive the expression for $$\mu$$^PG for a monatomic molecule (like argon) which has no internal structure and only has translational energy.

where $$\mu$$^PG is the perect gas contribution to the chemical potential.


(2)Treating the molecule N2 as a linear, rigid molecule is an excellent approximation.
Calculate numerical values of the perfect gas contribution to the molar entropy
and the molar isobaric heat capacity for N2 at 0 oC and 1 atmosphere. Justify any
contributions to the internal energy of the molecule that you omit from your
calculation.

For this i can plug the numbers in, i am just unsure of the equations to use.

 

[NateD]

The expression for the perfect gas contribution to the molar entropy is given by:\muPG = Rln(V/n) + RT Where V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. For N2 at 0 oC and 1 atmosphere, we have V=22.4 L/mol and n=1 mol, so the perfect gas contribution to the molar entropy is:\muPG = 8.314 x ln(22.4/1) + 8.314 x 273.15 = 7.842 kJ/molThe expression for the molar isobaric heat capacity is given by:Cp = R(5/2 + 1) For N2 at 0 oC and 1 atmosphere, we have R=8.314 J/molK and thus the molar isobaric heat capacity is:Cp = 8.314 x (5/2 + 1) = 30.036 J/molK We can ignore any contributions to the internal energy of the molecule because it is assumed that the molecule is at 0 oC and 1 atmosphere, which means that its internal energy is already accounted for in the thermal energy of the environment.