Relation between chemical potential and S,V,T,P

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Homework Help Overview

The discussion revolves around the relationship between chemical potential and thermodynamic variables such as entropy (S), volume (V), temperature (T), and pressure (P). The original poster explores the definition of chemical potential and its implications in thermodynamics, particularly in relation to the Gibbs-Duhem equation.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand the physical significance of the relationship between chemical potential and other thermodynamic variables. They express confusion about how this knowledge aids in the study of thermodynamics. Other participants provide insights into the Gibbs-Duhem equation and its relevance, particularly in multicomponent systems.

Discussion Status

Participants are engaging in a productive exploration of the topic, with some providing clarifications on the significance of chemical potential in different contexts. There is an acknowledgment of the relationship between intensive parameters and the implications for multicomponent systems, although no consensus has been reached on the original poster's specific questions.

Contextual Notes

There is a mention of the original poster's focus on a single-component system, which raises questions about the applicability of chemical potential in that context. The discussion also highlights the distinction between extensive and intensive parameters in thermodynamic equations.

Pushoam
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Homework Statement



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Homework Equations

The Attempt at a Solution

Chemical potential is defined as ## \mu = Gibbs potential per particle ##.

So, is the system consists of N particles, ##\mu = \frac { G } {N } ##.

Now, dG = VdP – SdT

## \frac {dG } { N } = \frac { VdP } { N } - \frac { SdT } { N}##

So, ## d{\mu} = -sdT + v dP##.

Hence the correct option is (a).

Is this correct?

I didn't get the physical significane of this question.
How does the knowledge of above eqn help us in our study of thermodynamics?
 

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Your answer is correct. This is the Gibbs-Duhem equation which tells us that for a simple system, the intensive parameters (T, P, μ) are not independent. Knowledge of 2 is enough to determine the 3rd up to an integration constant. Have a look at Wiki page too:
https://en.wikipedia.org/wiki/Gibbs–Duhem_equation
 
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Pushoam said:
I didn't get the physical significane of this question.
How does the knowledge of above eqn help us in our study of thermodynamics?
For the single component system you are considering, the chemical potential doesn't make much sense. But its value comes into play "big time" when you are considering multicomponent mixtures. It is used in describing multicomponent vapor-liquid equilibrium, multiphase equilibrium, and chemical reaction equilibrium. Be patient, and you will learn about this soon.
 
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Thanks for the reply.
The following eqn uses extensive parameters.
Pushoam said:
dG = VdP – SdT
.
We have derived the following eqn from the above eqn. One of the significance of the following eqn is: it consists of only intensive parameters.
Pushoam said:
## d{\mu} = -sdT + v dP##
 

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