Purchase Solution

Entropy and chemical potential

Not what you're looking for?

Ask Custom Question

For a diatomic gas near room temperature, the internal partition function is simply the rotational partition function multiplied by the degeneracy Ze of the electronic ground state.

(a) Show that the entropy in this case is

S = Nk [ln (VZeZrot/NvQ) + 7/2.

Calculate the entropy of a mole of oxygen (Ze = 3) at room temperature and atmospheric pressure, and compare to the measured value.

(b) Calculate the chemical potential of oxygen in earth's atmosphere near sea level, at room temperature. Express the answer in electron-volts.

Purchase this Solution

Solution Summary

A detailed solution is given.

Solution Preview

We can calculate the entropy from the partition function as follows. The partition function for an ideal gas is:

Z = Z1^(N)/N!

where Z1 is the partition function for a single molecule. Z1 factorizes:

Z1 = Z_{trans}*Z_{rot}*Z_{vib}*Z_{elec}*etc.

The translational part of the partition function is:

Z_{trans} = V*(2 pi m kT/h^2)^(3/2)

Since a partition function must be dimensionless the factor

(2 pi m kT/h^2)^(3/2)

must have the dimensions of an inverse volume. You can easily check this. This is the volume at which quantum effects become important. We define the quantity:

Vq = (2 pi m kT/h^2)^(-3/2)

to simplify expressions, but note that Vq depends on the temperature.

We ignore the vibrational part of the partition function and the electronic part is given by the degeneracy of the ground state, which ...

Purchase this Solution

Free BrainMass Quizzes
Basic Physics

This quiz will test your knowledge about basic Physics.

Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

The Moon

Test your knowledge of moon phases and movement.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.