Solving Enthalpy for Ideal Gas: Finding H as a Function of S and P

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SUMMARY

This discussion focuses on solving the enthalpy (H) for an ideal gas using the equation H = U + PV, where U is internal energy and PV is the pressure-volume product. The user seeks to express H as a function of entropy (S) and pressure (P). A key solution involves utilizing the Sackur-Tetrode equation, which relates the entropy of an ideal gas to internal energy (U), allowing for the inversion of this relationship to express U in terms of S. This enables the substitution back into the enthalpy equation, facilitating the desired expression.

PREREQUISITES
  • Understanding of thermodynamic equations, specifically H = U + PV
  • Familiarity with the Sackur-Tetrode equation for ideal gases
  • Knowledge of the relationships between entropy (S), internal energy (U), and pressure (P)
  • Basic concepts of ideal gas behavior and properties
NEXT STEPS
  • Study the Sackur-Tetrode equation in detail to understand its derivation and applications
  • Explore the relationship between internal energy (U) and entropy (S) for ideal gases
  • Research methods for expressing thermodynamic properties in terms of different variables
  • Examine additional thermodynamic identities and their implications for ideal gases
USEFUL FOR

Students and professionals in thermodynamics, chemical engineering, and physical chemistry who are working with ideal gas properties and seeking to deepen their understanding of enthalpy calculations.

quantoshake11
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Hello.
I'm having troubles solving the enthalpy for an ideal gas.
From the equation H=U+PV, i could find H substituting PV=NRT = U/c, but then i need the energy as a function of S and P, so i'd get H as a function of its proper variables (S and P)..
I can't find such an expression. It's just so easy to find the helmholtz and gibbs representation for ideal gases that i find it odd that this one gives me so much trouble. Wikipedia gives the equation for the enthalpy, but i have no clue how to write it that way :S
could anyone give me some clues to solve this one?
thanks
 
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There's an equation called the Sackur-Tetrode equation that expresses the entropy of an ideal gas S in terms of U. You can invert this to give U in terms of S, then substitute into your equation for H in terms of U and you will have H in terms of S.
 
oh, thanks! i just need to get the volume out of there, but i could use the other relations to do that. doh! i should've seen that earlier :P
 

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