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Chemical potential as a function of pressure

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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.

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

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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. ...

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