Chemical Potential: Heat Energy Carried by Particles

[iScience]

in class, we just learned that the chemical potential was μ=∂G/∂N

i'm looking in my book and it says that μ=-T(∂S/∂N) this looks a lot like the partial of heat energy with respect to N. is my interpretation correct?

(assuming my interpretation was correct): so qualitatively, the chemical potential is the heat energy carried by a constituent particle of a system?

 

[DrDu]

When taking the partial derivative, S is a function of what besides N?
Clearly you can write
$dS(V,U,N)=1/T dU+p/T dV + \mu/T dN$, so $\mu=T (\partial S/\partial N)_{V, U}$

 

[iScience]

okay silly question: where does the minus come from? Q=-TdS, but that minus gets canceled when rearranging to solve for dS like you did so then you end up with positive like you did.

 

[DrDu]

There may be different sign convention. The most common one which I also use is Q=TdS.

 

[PJC01]

Your interpretation is not entirely correct. The chemical potential, denoted by μ, is a thermodynamic quantity that represents the change in free energy, G, with respect to the change in the number of particles, N. It is related to the temperature, T, and entropy, S, of the system. The correct expression for the chemical potential is μ=-T(∂S/∂N), which is not the same as the partial of heat energy with respect to N.

In simple terms, the chemical potential represents the energy required to add or remove a particle from a system at constant temperature and pressure. It is a measure of the system's tendency to undergo a chemical reaction or phase change.

So, while it is related to heat energy, it is not the same thing as the heat energy carried by particles. Heat energy is a form of energy that is transferred between objects or systems due to temperature differences, while the chemical potential is a measure of the energy associated with the particles within a system.

In conclusion, the chemical potential is an important concept in thermodynamics that describes the energy changes associated with the number of particles in a system, but it is not the same as the heat energy carried by particles.