# Chemical potential as a function of pressure

Show that the equation:

μ (T, P) = μ° (T) + kT ln (P/P°)

is in agreement with the explicit formula for the chemical potential for a monatomic ideal gas. Show how to calculate μ° for a monatomic ideal gas.

© BrainMass Inc. brainmass.com June 3, 2020, 7:38 pm ad1c9bdddfhttps://brainmass.com/physics/second-law-of-thermodynamics/chemical-potential-function-pressure-106224

#### Solution Preview

In thermodynamics, everything can be derived from the Omega function that gives you the number of microstates compatible with a macrostate.

The derivatives of Log(Omega) w.r.t. the energy defines the temperature parameter:

beta = dLog(Omega)/dU (1)

The temperature is defined in terms of beta by:

beta = 1/(kT)

The derivative in (1) is at constant volume and constant number of particles.

If we differentiate w.r.t. ...

#### Solution Summary

A detailed solution is given. The expert examines chemical potential as a function of pressure.

$2.19