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

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The discussion centers on the challenge of deriving the enthalpy (H) for an ideal gas using the equation H=U+PV. The user expresses difficulty in expressing H as a function of entropy (S) and pressure (P), despite finding it straightforward for Helmholtz and Gibbs free energies. A suggestion is made to use the Sackur-Tetrode equation to express entropy in terms of internal energy (U), allowing for inversion to derive U as a function of S. The user acknowledges this approach and realizes they can eliminate volume from the equations using other relations. This exchange highlights the complexities of thermodynamic equations for ideal gases and the utility of established equations in simplifying the process.
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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