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chemical potential

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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 alot 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?

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