How do I solve this problem involving the Helmholtz and Gibbs Energy?

In summary, the conversation discusses the design of a system for controlling the pressure and volume of gas, filled with 1 gram of helium and compressed along a programmed path. The task at hand is to compute the initial and final temperatures, heat absorbed, work done, and changes in U, H, F, G, and S. The main challenge lies in expressing the equations for F and G without an entropy term, and potential solutions include using ideal gas absolute entropy or heats of formation. The individual seeking help is unsure of how to approach the problem and is open to any guidance.
  • #1
Zach Sims
1. Robert Dehoff 4.12
A system is designed that permits continuous programmed control of the pressure and volume of the gas that it contains. The system is filled with 1 g atom of helium and brought to an initial condition of one atmosphere and 18 liters. It is then reversibly compressed to 12 Liters along a programmed path given by the relationship.

V=2*P2+20

Where P is in atomospheres and V is in liters. Compute:
a Initial and Final temperatures
b Heat absorbed by the system
c The work done by the system
d The changes in U,H,F,G, and S

Homework Equations


There are many relevant equations to this problem. However, my main problem is the Gibb's and Helmholtz Energies. I have all the other values correct. The problem is I can't seem to find a way to express Gibb's and Helmholtz energy in a way that does not include an entropy term. I just don't know how to deal with them.

F = U-TS
G= H-TS

dH = 1520 J/mol
dU = 912 J/mol
T(initial)=215 K
T(Final)=292 K
dS = 0.26 J/(mol*k)

The Attempt at a Solution



I have been trying to write F as a function of T,P or V,P the problem is they always end up having some term of entropy. An example is my last attempt.

F(P,V) =-(S/P+P)dV+-S*(T/P)dP

And I just don't know how to solve these. I am just about to pull my hair out. I fee I am over complicating this and that the solution actually lies in a brief rearrangement of the relevant equation, but I cannot be sure.

Any help would be much appreciated.
 
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  • #2
Well, you need to determine ##\Delta (TS)##. But that is going to be a function of the value of S at some reference temperature. Are you allowed to use the ideal gas absolute entropy from statistical mechanics.? Or, are you allowed to use heats of formation, free energies of formation, and entropies of formation as being zero at 25 C and 1 atmosphere?
 
  • #3
Chestermiller said:
Well, you need to determine ##\Delta (TS)##. But that is going to be a function of the value of S at some reference temperature. Are you allowed to use the ideal gas absolute entropy from statistical mechanics.? Or, are you allowed to use heats of formation, free energies of formation, and entropies of formation as being zero at 25 C and 1 atmosphere?

I had a feeling that was the goal. I am not aware of any restrictions on the equations or paths we can take to a solution. I have tried to make an equation using the absolute entropy, but the equation seems at first confusing. Any guidance on how to first being my formulation would be much appreciated. Thanks.
 

1. What is the Helmholtz and Gibbs Energy?

The Helmholtz and Gibbs Energy are two thermodynamic potentials that describe the amount of energy available to do work in a system. They are related to each other through the equation F = U - TS, where F is the Helmholtz Energy, U is the internal energy, T is the temperature, and S is the entropy. The Gibbs Energy is related to the Helmholtz Energy through the equation G = F + PV, where G is the Gibbs Energy, P is the pressure, and V is the volume.

2. What is the difference between the Helmholtz and Gibbs Energy?

The main difference between the Helmholtz and Gibbs Energy is the conditions under which they are used. The Helmholtz Energy is used for systems at constant temperature and volume, while the Gibbs Energy is used for systems at constant temperature and pressure. This means that the Helmholtz Energy is more useful for closed systems, while the Gibbs Energy is more useful for open systems.

3. How do I calculate the Helmholtz and Gibbs Energy?

The Helmholtz Energy can be calculated using the equation F = U - TS, where U is the internal energy, T is the temperature, and S is the entropy. The Gibbs Energy can be calculated using the equation G = F + PV, where F is the Helmholtz Energy, P is the pressure, and V is the volume. Both of these equations require knowledge of the system's internal energy, temperature, entropy, pressure, and volume.

4. When is it appropriate to use the Helmholtz vs. Gibbs Energy?

The Helmholtz Energy is most commonly used for closed systems, such as a sealed container, where the volume is constant. It is also useful for systems at constant temperature and with no work being done. The Gibbs Energy is more useful for open systems, such as a reaction taking place in a beaker, where the pressure and volume can change. It is also useful for systems at constant temperature and pressure.

5. How can I use the Helmholtz and Gibbs Energy to solve a problem?

In order to use the Helmholtz and Gibbs Energy to solve a problem, you will need to have a clear understanding of the system and its conditions. You will also need to have knowledge of the equations F = U - TS and G = F + PV, and be able to rearrange them to solve for the desired variable. You may also need to use other thermodynamic equations and principles to fully solve the problem. It is important to carefully define all variables and units in order to get an accurate answer.

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