UPSC Exam  >  UPSC Notes  >  Chemistry Optional Notes for UPSC  >  Chemical Potential Can be Evaluated From a Partition Function

Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC PDF Download

Introduction

  • The chemical potential can be given in terms of a partition function. Internal energy can be defined as:
    Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC
  • And entropy can be defined as:
    Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC
    We know that Helmholtz energy is:
    A = U  − TS
    Using our two equations above, we obtain:
    A = −RT ln Q
  • Now, let's change gears a bit to show how Helmholtz energy is related to chemical potential. The total differential for Helmholtz energy is:
    Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC
    And the fundamental equation is:
    Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC
  • Using the relationship between Helmholtz energy and Gibbs energy:
    G = A + PV
  • We obtain:
    Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC
  • We know that the change in Gibbs energy is:
    Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC
    Inspecting these equations, we see that:
    Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC
  • This shows us that, as long as the natural variables for each thermodynamic potential are held constant, the partial derivatives of Gibbs energy and Helmholtz energy with respect to the number of moles,  n are equal to the chemical potential. We can now plug in our expression above for Helmholtz energy in terms of the partition function:
    Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC
    We now have chemical potential written in terms of the partition function, Q.
The document Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC is a part of the UPSC Course Chemistry Optional Notes for UPSC.
All you need of UPSC at this link: UPSC
308 docs

Top Courses for UPSC

308 docs
Download as PDF
Explore Courses for UPSC exam

Top Courses for UPSC

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Important questions

,

Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC

,

Free

,

Semester Notes

,

MCQs

,

Exam

,

past year papers

,

Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC

,

study material

,

Sample Paper

,

Extra Questions

,

pdf

,

video lectures

,

Previous Year Questions with Solutions

,

ppt

,

Viva Questions

,

Summary

,

Objective type Questions

,

Chemical Potential Can be Evaluated From a Partition Function | Chemistry Optional Notes for UPSC

,

practice quizzes

,

shortcuts and tricks

,

mock tests for examination

;