Chemical potential as function of height in Earth's gravity
Not what you're looking for?
See attached file.
Purchase this Solution
Solution Summary
A detailed solution is given.
Solution Preview
You need to use these formulas for the potential and kinetic parts of the internal energy in the formula of the entropy. The fundamental law of thermodynamics is:
dU = T dS - PdV + mu dN
From this you read off that
mu = -T(dS/dN)_U,V (1)
Let's first consider how the formula for the entropy will change if we include the potential energy due to the height. If you recall the derivation of the formula for the entropy:
S = k Log[Omega]
with
Omega = V^(N)/h^(3N) Integral d^(3N)p
where the momentum integral is over a shell in momentum space that corresponds to a certain internal energy of the gas, then it should be clear that you now need to substitute the kinetic part of the internal energy in that formula instead of the total internal energy, because the kinetic part fixes the shell in momentum space. The kinetic part of the total internal energy is, of course:
U_kin = U - mgzN
And the formula for the entropy ...
Purchase this Solution
Free BrainMass Quizzes
The Moon
Test your knowledge of moon phases and movement.
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.
Basic Physics
This quiz will test your knowledge about basic Physics.
Classical Mechanics
This quiz is designed to test and improve your knowledge on Classical Mechanics.
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.