Thermodynamics(math) derivation step

  • Thread starter Thread starter iScience
  • Start date Start date
  • Tags Tags
    Derivation
Click For Summary
SUMMARY

The discussion focuses on a specific step in a thermodynamics derivation involving the cancellation of terms, specifically the -(q+N) term and its subsequent cancellation with +q and +N. The user seeks clarification on how terms within the natural logarithm (ln) can be extracted, referencing "Stirling's approximation" as a key concept. The derivation illustrates the application of Stirling's approximation in simplifying expressions involving large factorials, which is crucial for understanding thermodynamic equations.

PREREQUISITES
  • Understanding of thermodynamic principles and equations
  • Familiarity with Stirling's approximation
  • Basic knowledge of logarithmic functions
  • Experience with mathematical derivations in physics
NEXT STEPS
  • Study the application of Stirling's approximation in statistical mechanics
  • Explore the properties of logarithmic functions in mathematical derivations
  • Review thermodynamic identities and their derivations
  • Investigate the role of large numbers in thermodynamic calculations
USEFUL FOR

Students and professionals in physics, particularly those studying thermodynamics and statistical mechanics, will benefit from this discussion as it clarifies complex derivation steps and the application of mathematical approximations.

iScience
Messages
466
Reaction score
5
hi, i just need help with a step in a derivation in my thermodynamics book (indicated by the red arrow)



http://i.imgur.com/C8k3xzT.jpg

firstly, what's the point of a -(q+N) term if they're just going to cancel it out with a +q and +N?

basically i want to know how the terms inside the 'ln' can come out in front.
 
Physics news on Phys.org

Similar threads

How Does the Sackur-Tetrode Equation Resolve the Gibbs Paradox?
  • · Replies 4 ·
Replies
4
Views
5K
Entropy of spin-1/2 Paramagnetic gas
  • · Replies 7 ·
Replies
7
Views
4K
Deriving Fermi-Dirac Distribution misunderstanding
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Derivation of Equation 26 in Bardeen's Four Laws of Black Hole Thermodynamics
  • · Replies 1 ·
Replies
1
Views
1K
Deriving the Adjoint / Tangent Linear Model for Nonlinear PDE
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Zeroth law of black hole thermodynamics
  • · Replies 9 ·
Replies
9
Views
2K
MHB Trouble finding the derivative of a fraction using four step process
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Partial derivatives of thermodynamic state functions
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Commutation between covariant derivative and metric
  • · Replies 16 ·
Replies
16
Views
4K
Math Problem Issue: Deriving 4.12 from 4.11
  • · Replies 1 ·
Replies
1
Views
2K