# What is Helmholtz free energy: Definition and 41 Discussions

In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium.
In contrast, the Gibbs free energy or free enthalpy is most commonly used as a measure of thermodynamic potential (especially in chemistry) when it is convenient for applications that occur at constant pressure. For example, in explosives research Helmholtz free energy is often used, since explosive reactions by their nature induce pressure changes. It is also frequently used to define fundamental equations of state of pure substances.
The concept of free energy was developed by Hermann von Helmholtz, a German physicist, and first presented in 1882 in a lecture called "On the thermodynamics of chemical processes". From the German word Arbeit (work), the International Union of Pure and Applied Chemistry (IUPAC) recommends the symbol A and the name Helmholtz energy. In physics, the symbol F is also used in reference to free energy or Helmholtz function.

View More On Wikipedia.org
1. ### I Why does Callen insist a process must be reversible here?

In a discussion about the (change in the) Helmholtz potential being interpretable as the maximum available amount of work for a system in contact with a thermal reservoir (i.e. the free energy), Callen seems to insist this fact is true only for reversible processes. Why should this be? I...
2. ### I Another question from Ashcroft and Mermin: Fermi-Dirac Distribution

Good Day : i reached the page 40 of Ashcroft Mermin book and after the equation 2.38 there is this expression of E(a,N) which is equal to Helmoltez Free energy F = U - TS , how this two terms F , E are related ? anyone can provide adequate explanation , and few useful references Best...
3. ### Helmholtz free energy for mixing?

Hi, I have been reading a few literature regarding excess Helmholtz energy and I encountered this definition from the paper of Wong and Sandler (apparently, from the mixing rule used in a EOS): In particular, the ones in the red boxes. How did these equations come into being? I tried to look...
4. ### Liquid-solid transition

Hello! I'm struggling with this exercise for three days already. Would appreciate any help. Thanks in advance. This is my thoughts... So a number density ρ=N/V. As I understand N doesn’t change through transition, but V changes The free energy F=U-TS or dF=-PdV-SdT As the liquid coexists...
5. ### Entropy and the Helmholtz Free Energy of a Mass-Piston System

Attempt at a Solution: Heat Absorbed By The System By the first law of thermodynamics, dU = dQ + dW The system is of fixed volume and therefore mechanically isolated. dW = 0 Therefore dQ = dU The change of energy of the system equals the change of energy of the gas plus the change of energy...
6. ### I Helmholtz free energy concept

This is really basic,and I’m not seeing something obvious,but I’d appreciate help with this concept. In differential form dA= -tds-pdv. However s and v are the natural variables for this free energy and are held constant . As I understand it the Helmholtz free energy is the energy available to...
7. ### Equilibrium volume of two differential van der Waal gases

Homework Statement Two ideal van der Waals fluids are contained in a cylinder, separated by an internal moveable piston. There is one mole of each fluid, and the two fluids have the same values of the van der Waals constants b and c; the respective values of the van der Waals constant ''a'' are...
8. ### Where is the work done coming from in Helmholtz free energy

Sorry,i want to ask a question here the note said the volume is "fixed" here. if the volume if fixed,how comes the work done(because no change of volume) here i totally get lost here thank
9. ### Helmholtz and Gibbs free energy for an adiabatic process

Homework Statement Calculate changes in A and G of one mole of an ideal gas that undergoes the following processes respectively. 1. adiabatic expansion from (T1, P1) to (T2, P2) 2. isobaric expansion from (P, V1, T1) to (P, V2, T2) (if it is not isothermal) 3. isochoric expansion from (V, P1...
10. ### I Helmholtz Free Energy: Why is F Minimized?

Hello! I read that the Helmholtz free energy is minimized at constant T and V at equilibrium. But I am not sure I understand why. So starting from ##F=U-TS## I got ##dF = \mu dN - pdV -SdT##. So at constant V and T we have ##dF = \mu dN##. Now I am not sure how does this implies that F is...
11. ### Problem on Thermodynamics

Homework Statement Derive the equation ##U=-T(\frac{\partial A}{\partial T})_V## where ##U## is the internal energy, ##T## is the temperature, ##A## is the Helmholtz function. Reference: Heat and Thermodynamics, Zemansky, Dittman, Page 272, Problem 10.4 (a) Homework Equations ##dA=-PdV-SdT##...
12. ### Is there an Altitude Dependence on Helmholtz Free Energy?

Homework Statement [/B] The density of nitrogen molecules is larger at a sea level than at a higher elevation. Assuming thermal equilibrium, what is the altitude dependence of the (Helmholtz)free energy per particle? Homework Equations F=U-TS, not sure if anything else is relevant The Attempt...
13. ### Helmholtz free energy problem

Homework Statement Homework Equations Maxwell relations The Attempt at a Solution I have an attempt at a solution, but I am not sure if I can replace the integral of dT in the helmholtz equation by the T I found using the internal energy. Does this make sense? Thanks
14. ### Specific Heat and Helmholtz Free Energy?

I'm wondering if there's a simple relation between the specific heat capacity (at constant chemical potential) and the Helmholtz Free Energy? I can't seem to find a relation in the literature between these three quantities, specifically.
15. ### Magnetic moment of paramagnetic crystal

Hello, I've been having some trouble with a paramagnetism problem from my Statistical Mechanics class textbook (F. Mandl, Statistical Physics, 2nd edition, p. 25). The problem is as follows 1. Homework Statement 2. Homework Equations 1. The temperature parameter \displaystyle{ \beta =...
16. ### Helmholtz Free Energy Legendre Transformation

Homework Statement Show how a Legendre transformation is used to obtain the Helmholtz free energy A(T,V) from the internal energy and derive the general expression for the differential of A. Homework Equations Internal Energy is a function of Entropy and Volume. U Ξ (S, V) A Ξ (T,V) A = U...
17. ### Helmholtz free energy in the canonical ensemble

Hello everybody :D My question is: given the distribution of the canonical ensemble, how do we get the helmoltz free energy? I think we can't use A = U-TS because we don't know how to write S. So what's the solution? Thanks
18. ### The grand potential and total Helmholtz free energy

what's the relation of the grand potential J=F-\mu N and total Helmholtz free energy of "system and particle environment" F^{tot}? In K. Sekimoto's book "Stochastic Energetics" P182, P310 and P311 (see screenshots in the link): Does it mean the followings:J=lim[F_{tot}-\mu N_{tot}]...
19. ### Derive Internal Energy from Thermodynamic Identity

Homework Statement For a single molecule, derive the internal energy U = 3/2kBT In terms of the partition function Z, F = -kBTlnZ Where Z = V(aT)3/2 Homework Equations Thermodynamic identity: δF = -SδT - pδV p = kBT/V S = kB[ln(Z) + 3/2]The Attempt at a Solution U = F + TS δU = δF +...
20. ### Enthelpy ,gibbs free energy, helmholtz free energy

To analyze what does the enthalpy, gibbs free energy and helmholtz free energy are used?What is actually meant by usable energy?
21. ### Helmholtz free energy of simple solid

The problem is : a) Find Helmholtz free energy F(V, T) of a simple solid. b) Use the result of part a) to verify that (∂F/∂T)v and (∂F/∂V)T are consistent with S(T, V) and P(V, T) in equation P=a0T-b0ln(V/V0) I know: Helmholtz free energy is F=U-TS and dF=-SdT-PdV S=-((∂F/∂T)v)...
22. ### Find an Expression for the Helmholtz free energy

Homework Statement I am attempting the problem below, I might have the correct answer but would appreciate if someone could confirm this (or tell me where I'm going wrong). Consider a statement having 2 states, one at energy 0 and one at energy ε. Find an expression for the Helmholtz free...
23. ### Temperature CONFUSION in derivation for Helmholtz Free Energy

Dear all, I have been spending 12 hours on this and cannot seem to come up with a solution. We derive Helmholtz Free Energy (A) from the second law of thermodynamics. dS(Total) = dS(system) + dS(surrounds) we try to express dS(surrounds) with properties of the system. Assuming...
24. ### Stability, Helmholtz free energy mathematical relation proof

Stability, Helmholtz free energy mathematical relation "proof" Homework Statement I must show that \left ( \frac{\partial ^2 F}{\partial V ^2} \right ) _T=\frac{\frac{\partial ^2 U}{\partial S^2} \frac{\partial ^2 U}{\partial V ^2} - \left ( \frac{\partial ^2 U}{\partial S \partial V} \right...
25. ### Difference between enthelpy, Helmholtz free energy,& Gibbs free energy

I am study chapter 5 of An Introduction to Thermal Physics by Schroeder and I am having trouble understanding his explanation of the differences between enthaply, Helmholtz free energy, and Gibbs free energy. Schroeder defines enthalpy of a system as its energy plus the work needed to make...
26. ### Helmholtz free energy related query.

hello This is a section from Callen, Herbert B - Thermodynamics and an Introduction to Thermostatistics "Any equilibrium state can be characterized either as a state of maximum entropy for given energy or as a state of minimum energy for given entropy. But these two criteria nevertheless...
27. ### Do not understand Helmholtz free energy

I'm currently learning thermodynamics from Schroeder's "An Intoduction to Thermal Physics". He explains that in an environment of constant temperature, the system can extract heat from the environment for free when we create a system, and the Helmholtz free energy is that additional work needed...
28. ### Helmholtz free energy

Is defined as F = U - TS and it is the energy needed to create a system minus the heat it can get for free. But why is the heat that it can get for free given by: Q = TS I know the thermodynamic relation: S = Q/T So in that way I understand it. But how do you know, that the system will be...

I'm having some trouble understanding this concept. Why is it that you sometimes can get heat for free from the environment? Like suppose you have a system, on which you make an energyconsuming proces which creates entropy. Then you subtract TΔS because apparently heat can enter when the entropy...
30. ### Thermodynamics, Helmholtz free energy, Legendre transformation

Homework Statement The Helmholtz free energy of a certain system is given by F(T,V) = -\frac{VT^2}{3}. Calculate the energy U(S,V) with a Legendre transformation. Homework Equations F = U - TS S = -\left(\frac{\partial F}{\partial T}\right)_V The Attempt at a Solution We...
31. ### Understanding the Helmholtz free energy, what does 'useful work' really mean?

When it comes to thermal/statistical mechanics, I'm a little retarded... so bear with me please. I've used the helmholtz free energy (F) dozens of times, almost as many times as I've heard and read that F is a measure of the 'useful work attainable from a closed thermodynamic system,' at...
32. ### Helmholtz Free Energy: Finding C_H-C_M Relation

Homework Statement The Helmholtz free energy is written as: dA=-SdT-pdV-VMdH when an incompressible liquid is placed in a magnetic field H. Thus, the free energy can be written as since -pdV=0: dA=-SdT-VMdH The two heat capacities can be defined as: C_H = T (dS/dT)_H and C_M = T...
33. ### Minimising helmholtz free energy

Homework Statement Show that the most probable energy minimises the Helmholtz free energy. Homework Equations F=E-TS(E) where S(E) is the entropy of te system of given energy E. The Attempt at a Solution Not sure how you would 'show' is ? P(E) = 1/Z *weight funciton*exp(-beta E)
34. ### Thermodynamics: Helmholtz free energy

Homework Statement Hi all. Lets take a look at the Helmholtz free energy. It is defined as the amount of energy one has to put into create a system once the spontaneous energy transfer to the system from the environment is accounted for. Now let's look at it once we have created the...
35. ### Reason behind the definition of Helmholtz free Energy

What is the reasoning behind defining the helmholtz free energy as F = -kT ln Z? I always wanted to know why it was just defined as the above. Is it as a form of convenience because the macroscopic theromodynamic observables of a system at constant temperature (ie the canonical ensemble) are...
36. ### Helmholtz free energy decreases

Helmholtz free energy decreases... Hello... I'm having trouble getting my head around something. I'm not exactly sure what is meant by the Helmholtz free energy (F) decreasing in a system that's in thermal equilibrium with it's environment. Under what circumstances does it decrease...
37. ### Statistical mechanics - Helmholtz free energy and Z

Homework Statement The neutnral carbon atom has a 9-fold degeerate ground level and a 5-fold degenerate excited level at an energy 0.82 eV above the ground level. Spectroscopic measurements of a certain star show that 10% of the neutral carbon atoms are in the excited level, and that the...
38. ### Helmholtz Free Energy

\tau = k_{B} T a) Find the expression for the free energy as a function of the temperature of the system with two states - one iwth eneryg zero and one with energy \epsilon_{0} b) From the free energy find the expressions for the energy and entropy of the system c) Plot the average energy...
39. ### Helmholtz free energy question

what's the physical meaning of that equation? all i see is a jumble of numbers and equations...
40. ### Helmholtz free energy question

for the proof of the helmholtz free energy question, why is q smaller or equal to T(S2-S1)?
41. ### Calculate Helmholtz Free Energy Change from Data

Let’s say we have a 1 mol system in a state A (Pa,Va,Ta are given) and we take it to a state B(Pb,Vb are given) . We want to know what’s the maximum work we can give to a reversible work source. Considering the process is carried out attached to a 150 K heat source, the only data available is...