# What is Helmholtz energy: Definition and 12 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.

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1. ### DeltaG and DeltaA calculation for heating a gas at constant volume

Summary:: Gibbs and Helmholtz energies calculations for heating an ideal gas at constant volume I am solving a problem involving an ideal gas that undergoes several chained changes of state. One of the steps asks to calculate the change in Gibbs Energy (DeltaG) and Helmholtz energy (Delta A)...
2. ### Chemistry How Does Surface Area Affect the Free Energy of a Liquid?

Hello, so first of all I want to clarify that english is not my first lenguage, so I'm really sorry for possible future errors. Second, this is a problem from my physical chemistry class, and I'm not sure where it fits better, if here or in the physics homework help, I'm sorry :( So, I don't...
3. D

### Free energy Helmholtz using only the equation of state

Homework Statement This is a state ecuation of a gas: PV=AT+B/V, where A and B there are constants. First: Demonstrate that ##c_V## depends only of T Second: Find U(T,V) and S(T,V) Homework Equations ##\left(\frac{\partial U}{\partial S}\right)_V=T\text{ (1)}## ##\left(\frac{\partial...
4. ### Proving Minimization of Helmholtz Free Energy at Equilibrium

Homework Statement Show that for a reaction occurring at constant T and V, F is minimized at equilibrium. Homework Equations ##F=U-TS## ##TdS=dU+pdV-\mu dN## The Attempt at a Solution ##dF=dU-d(TS)=dU-TdS-SdT=dU-dU -pdV+ \mu dN -S dT=-pdV - SdT + \mu dN##. At constant T and V this reduces to...
5. ### Derivation of Helmholtz Energy Minimum in Thermodynamics

Hey, The helmholtz energy is supposed to have a minimum when the entropy has a maximum value. Does anyone knows the derivation for this statement?
6. ### Helmholtz 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)...
7. ### Calculation of Helmholtz energy

Homework Statement The 4 fundamental equations of thermodynamics are: dE = TdS - PdV dH = TdS + VdP dG = VdP - SdT dA = - PdV - SdT Supose a gas obeys the equation of state P = \frac{nRT}{V} - \frac{an^{2}}{V^{2}} Use one of the fundamental equations to find the change in Helmholtz energy...
8. ### Helmholtz Energy Proof (thermodynamics)

Homework Statement Define the Helmholtz free energy as F=E-TS. Show that the internal energy E=-T2\frac{∂}{∂T}(\frac{F}{T})V Homework Equations S=(\frac{∂F}{∂T})V Perhaps \beta=\frac{1}{\tau} and \tau=kBT The Attempt at a Solution E = F+TS E = F+T(\frac{∂F}{∂T})V . . . (some...
9. ### Fundamental Thermodynamic Relation and Helmholtz Energy

I'm confused about the condition for spontaneity for the Helmholtz energy. My textbook (McQuarrie, "Physical Chemistry") derives the conditions as follows. We start with the combined law of thermodynamics: dU = δq + δw ≤ TdS – PdV since δq/T ≤ dS dU – TdS + PdV ≤ 0 For a process at...
10. ### Calculating Helmholtz energy (incl degeneracy)

Hi I'm trying to calculate Helmholtz free energy from definition \frac{\partial A}{\partial T}=\frac{\partial}{\partial T}(kT\mathrm{ln}\; Z). First \langle E\rangle=\sum\limits_i p_i E_i=\sum\limits_i E_i\frac{g_i e^{-\beta E_i}}{Z}=\frac{1}{Z}\sum\limits_i E_i g_i e^{-\beta...
11. ### Understanding the Helmholtz energy.

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...
12. ### How does the Helmholtz energy formula intuitively make sense?

Homework Statement Explain why the formula (dF/dV)=-P , where T and N are constant variables , makes intuitive sense, by discussing graphs of F vs. V with different slopes. Homework Equations The Attempt at a Solution dF=SdT-PdV+mu*dN dT and DN are zero since T and N are...