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

In summary, the conversation discusses the difficulties in finding the enthalpy for an ideal gas and how it can be solved using the Sackur-Tetrode equation. The equation expresses the entropy of an ideal gas in terms of U, which can then be inverted to give U in terms of S. Substituting this into the equation for H in terms of U will give H in terms of S.
  • #1
quantoshake11
45
0
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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  • #2
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.
 
  • #3
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
 

1. What is enthalpy and why is it important?

Enthalpy is a thermodynamic property that describes the total energy of a system, including its internal energy and the work required to maintain a constant pressure. It is important because it helps us understand and predict the behavior of chemical reactions, as well as the energy changes involved in processes such as combustion, phase transitions, and formation of solutions.

2. How do you calculate enthalpy for an ideal gas?

For an ideal gas, enthalpy can be determined by using the equation H = U + PV, where H is enthalpy, U is internal energy, P is pressure, and V is volume. This equation takes into account the work done by the gas on its surroundings and the work done on the gas by its surroundings.

3. Can enthalpy be negative for an ideal gas?

Yes, enthalpy can be negative for an ideal gas. This indicates that the gas has lost energy, either through a decrease in internal energy or a decrease in the work done by the gas.

4. How does enthalpy change with temperature and pressure?

Enthalpy is directly proportional to temperature for an ideal gas, meaning that as temperature increases, so does enthalpy. However, enthalpy is not affected by changes in pressure for an ideal gas, as long as the volume remains constant.

5. How can I solve for enthalpy using entropy and pressure?

You can use the equation H = U + PV and the ideal gas law (PV = nRT) to solve for enthalpy. By substituting PV for nRT in the enthalpy equation, you can rearrange the equation to solve for enthalpy in terms of entropy and pressure. The resulting equation is H = U + nRTln(P), where n is the number of moles of gas and ln is the natural logarithm.

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