Free energy Definition and 302 Threads

The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether a process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.
The free energy is a thermodynamic state function, like the internal energy, enthalpy, and entropy.

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  1. E

    Is Gibbs free energy just potential energy reduction?

    So I know that things in the Universe tend to move toward a state of least potential energy. This is why forces point in the direction of decreasing potential energy, as everything is trying to minimize its potential energy. So my main question is: does Gibb's free energy basically just...
  2. I

    Is the minimum Gibbs free energy the same for every material?

    We were learning about the change in free energy in class, but I was wondering since the Gibbs free energy decreases as a system becomes more stable, is the minimum absolute free energy for a material the same for every material, or can other materials be more stable than others?
  3. C

    A Free energy density in liquid crystals

    Hi, For someone who's familiar with LC's: How to derive the expression for free energy density of an hybrid aligned LC cell? what should be the vector for the director? I already familiar with the cases of splay and bend cell but couldn't understand how to derive it to the case where the cell is...
  4. A

    Estimating Vapor Pressure of Mercury at 25°C Using Appendix D Data

    Homework Statement Estimate the vapor pressure of mercury at 25 ∘C (use data from Appendix D from the textbook). Homework Equations Using the appendix I can find ΔG, ΔH, and ΔS. The Attempt at a Solution I have no idea where to start. I think that maybe vapor pressure would be found when...
  5. A

    How to Calculate Total Pressure in a Chemical Equilibrium System?

    Homework Statement Introduced into a 1.70 −L flask is 0.120 mol of PCl5(g); the flask is held at a temperature of 227∘C until equilibrium is established. PCl5(g)⇌PCl3(g)+Cl2(g) What is the total pressure of the gases in the flask at this point? [Hint: Use data from Appendix D in the textbook...
  6. S

    Generator efficiency in a vacuum

    If you had a generator in a vacuum with a magnetically levitated rotor and power was drawn from the system by induction, use your imagination on the design of the device, but my question is: Where are the flaws in this concept? (Since perpetual machines are theoretically impossible). In other...
  7. R

    Gibbs free energy -- mathematical expression

    I am not able to understand the mathematical expression of "change in Gibbs free energy", For a chemical reaction occurring at constant temperature and constant pressure, (ΔS)total = (ΔS)system + (ΔS)surrounding Considering that reaction is exothermic, ΔH be the heat supplied by system to...
  8. Narayanan KR

    Half Electrolysis: Battery & Choke Coil Setup

    CONSTRUCTION: -In the following figure a metal plate is immersed in a Trough of salt water, the wire hooked to plate is attached to a choke coil and the other end of choke coil is Grounded deep inside soil. -A...
  9. B

    What Are the Standard Enthalpy and Entropy Changes for the Graphed Reaction?

    Homework Statement My questions are based on a graph. I am trying to figure out the standard ΔH change for the graphed reaction and the standard entropy change. (1) What is the standard enthalpy change for the graphed reaction? (A) -31 KJ/mol (B) 0 (C) +12 KJ/mol (D) +11 KJ/mol (2) What is...
  10. A

    Gibbs Free Energy, Maxwell Relations

    Homework Statement We have a Gibbs Free Energy function G=G(P, T, N1, N2) I am not writing the whole function because I just want a push in the right direction. Find expressions for the entropy, volume, internal energy, enthalpy and chemical potential. Homework Equations Maxwell Relations...
  11. Y

    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...
  12. T

    Freezing/Melting of water and gibbs free energy

    Hello, I get that ΔG measures the spontaneity/capacity of a system to do non-mechanical work, and that if: ΔG>0, the reaction is not spontaneous ΔG<0, the reaction is spontaneous ΔG=0, the reaction is at equilibrium So why is Gibbs free energy zero for phase changes at constant temperature and...
  13. wololo

    What is the solution for finding F in terms of T and V without integrating?

    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. Eureka99

    Trouble with Gibbs free energy equation

    Hi everybody! Lately I tried to overcome some problems with understanding thermodynamics laws, and unfortunately I couldn't find anything about my question:nb) and I really hope someone can help me here... My question is: This version of Gibbs formula dG= VdP-SdT, can be applied to any close...
  15. T

    Does Gibbs Free Energy play a role in the storage of energy in ATP?

    Hello, Gibbs free energy describes the maximum of useful work that can be done by a chemical reaction. My question is(Sorry I am not into chemistry and biochemistry) : during a chemical reaction that creates ATP, we say that ATP stores energy between its chemical bonds . For exemple this is the...
  16. T

    Gibbs Free Energy and maximum work

    Hello, The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process. This maximum work is equal to H-TS. My question is this TS energy is what kind of energy? and from where it...
  17. M

    Internal Energy/Helmholtz Free Energy Proof

    Homework Statement Show that (∂(βA)/∂β)N,V = E, where A = E - TS is the Helmholtz Free Energy and E is the Internal Energy. Homework Equations A = E - TS dE = TdS - pdV + ΣUidni β = 1 / (kBT) The Attempt at a Solution (∂(βA)/∂β)N,V = (∂/∂β) * (βE - βTS) (∂(βA)/∂β)N,V = (∂/∂β) * (βE -...
  18. R

    Gibbs free energy various forms

    What is the difference between 1) ΔG°' and ΔG° and 2) ΔG°' and ΔG ? ΔG° I think it is the gibbs free energy at standard state means at room temperature 1 atm pressure.
  19. P

    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.
  20. Paulo Bernardo

    Meaning of Free Energy (Gibbs free energy)

    Hello everyone, I'm reading some basics of chemistry thermodynamics, and it's hard for me to figure out what is the actual meaning of free energy. could someone please help clarifying this giving specify, real life examples, like applications in mechanical engineering. Thanks
  21. S

    Is ΔG always equal to 0 when ΔSsystem ≠ 0 and qP = 0?

    ΔG=ΔH-TΔSsystem and ΔSsystem=qp/T and isn't qp=ΔH? Which means ΔG=0 always which is obviously wrong. But the derivation for Gibbs Free Energy is based on qsurrounding=-qsystem so shouldn't the term be equals to 0?
  22. S

    Gibbs Free Energy for non-standard conditions

    ΔG=ΔG°+RTlnQ are for reactions that are not under standard conditions. What does it mean under non-standard conditions for the ΔG? And what is the Q in this case? Is it Qp where it is based on the partial pressure of the gas or Qc which is based on the concentration? Thanks
  23. S

    Decomposition potential and Gibbs Free Energy

    The decomposition potential is always higher than the theoretically determined potential by thermodynamics. E=η+Eeq where E is the decomposition potential, η is the overpotential and Eeq is the theoretically determined potential. And ΔG=-nFE and if we were to substitute the decomposition...
  24. S

    Decomposition potential and Gibbs Free Energy

    The decomposition potential is always higher than the theoretically determined potential by thermodynamics. E=η+Eeq where E is the decomposition potential, η is the overpotential and Eeq is the theoretically determined potential. However since the decomposition potential is higher doesn't it...
  25. M

    Analytical continuation free energy

    Hi All, reading a paper by Langer (Theory of the Condensation Point, Annals of Physics 41, 108-157, 1967), I came across an analytical continuation technique which I do not understand (would like to upload the paper PDF but I am not so sure this is allowed). Essentially, he deals with the...
  26. S

    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...
  27. K

    Is Free Energy Possible Through Tesla's Discoveries?

    I am not a physicist but I do have a question, is it really possible to have zero point energy? Is the free energy related to Tesla the same thing as dark energy? When you are taught physics in college are you taught something like that? (planning to start physics as a career by next year) and I...
  28. X

    Landau Free Energy -- Phase transistions

    Homework Statement Consider the Landau free energy ##\mathcal{L}=-hm+r_1 t m^2+Cm^3+s_0 m^4## with an additional ##m^3## term. We consider zero magnetic field case ##h=0## and ##s_0>0##. a.) Please show that there are two critical temperatures ##t*## and ##t_1##. When ##t<t*##, a second...
  29. C

    Construction of free energy using Landau theory

    Consider an Ising model system where the total energy is ##E = −J \sum_{<ij>} S_iS_j ##, ##S_i = \pm 1## and ##< ij >## implies sum over nearest neighbours. For ##J < 0## the ground state of this system at ##T = 0## is antiferromagnetic. (All adjacent spins misaligned so net magnetisation zero...
  30. C

    Landau Free Energy & Ising Model at T=0

    Homework Statement The total energy of the Ising model is ##E = −J \sum_{<ij>} S_iS_j ##, where ##S_i = \pm 1## and ##< ij >## implies sum over nearest neighbours. For ##J < 0## explain why the ground state of this system at ##T = 0## is antiferromagnetic. Let ##m_{1,2}## be the magnetisations...
  31. B

    How Is Standard Gibbs Free Energy Calculated for Water Vapor Formation?

    Homework Statement What is the standard Gibbs free energy of formation of water vapor at 25 C if for the reaction shown below under standard conditions, ΔH = -484 kJ/mol and ΔS=-89 J/mol K? 2H2 + Os→2H2O Homework Equations ΔG = ΔH-TΔS The Attempt at a Solution Usually I can do these problems...
  32. G

    Gibbs free energy and equilibrium constant at a high T

    I posted this earlier, but I just realized it might have been in the wrong section. Sorry Okay, so consider you have system in which ΔG<0 and ΔS>0. Using Gibbs free energy (ΔG=ΔH-TΔS), you'll know that it will always be negative. As the temperature increases, it will actually become more and...
  33. E

    Understanding Gibbs Free Energy Curves: Homework Statement & Equations

    Homework Statement Can anyone explain to me the gibbs free energy curve? Homework EquationsThe Attempt at a Solution [/B] What is the domain of the curve and how should I interpret it?Thanks.
  34. A

    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
  35. T

    Gibbs Free Energy in Superconductors

    When reading some material concerning Ginzburg-Landau theory of superconductors, I got the following sentence: The appropriate thermodynamic potential for describing a superconductor in an applied magnetic field is the Gibbs free energy ##G## (natural variable ##H##) and not the Helmholtz free...
  36. 8008jsmith

    Standard Free Energy of Activation of a Reaction

    Homework Statement The standard free energy of activation of a reaction A is 83.7 kJ/mol at 298K. Reaction B is 10 million times faster at the same temperature. The products of each reaction are 10 kJ/mol more stable than the reactants. (a) What is the standard free energy of activation of...
  37. U

    Thermodynamics: Enthelpy vs. Gibbs Free Energy usage

    I'm currently taking a Biophysics lecture. There's a vast usage of the terms Enthalpy and Gibbs Free Energy. I understood that most of the time, we're dealing with the Gibbs Free Energy, because our experiment is at constant Temperature (e.g. room temperature) and constant Pressure (e.g. 1 atm)...
  38. F

    Minimal of free energy equation

    Homework Statement Show that the free energy, F=SUM(E_i*p_i)+T*SUM(p_i*ln(p_i)) is minimal when p_i=e^(-E_i/T)/SUM(e^(-E_i/T)) Where E is energy, T is temperature Homework Equations Nothing really The Attempt at a Solution So if I just try and find the derivative of the force I arrive at...
  39. X

    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}]...
  40. B

    In Gibbs Free Energy, why multiply -T?

    When you get the equation for the Gibbs free energy, why do you multiply -T? Can't you multiply just T? I thought about this and came up with an answer of my own, which goes like 'Because its Gibbs 'Free' Energy, when you have that free energy ( \Delta G >0) you have the energy to do...
  41. MexChemE

    Free energy in the free expansion of an ideal gas

    Hello PF! Consider the free expansion of an ideal gas. The process occurs at constant temperature, therefore, ΔU = 0, Q = 0, and W = 0. Suppose we are given the initial and final pressures of the gas, and we calculate ΔG = nRT ln(P2/P1). As P2 < P1, ΔG < 0. This is intuitive, as a free expansion...
  42. MexChemE

    Gibbs free energy and entropy inconsistency

    Homework Statement For a certain reaction, ΔG = 13580 + 16.1 T log10(T) - 72.59 T. Find ΔS and ΔH for the reaction at 298.15 K. Homework Equations ΔG = ΔH - TΔS \left[\frac{\partial (\Delta G)}{\partial T} \right]_P = - \Delta S The Attempt at a Solution For the sake of this thread's length I...
  43. ChristineMarie

    Molar Free Energy of an Ideal Gas at Temperature T and Pressure P

    Homework Statement Derive an equation for the change in free energy, ΔGmixing, when ideal gases with the same temperature and pressure, are mixed. Homework Equations ΔGmixing = nRT∑(xi)ln(xi) (∂/∂T(G/T))p = -H/(TxT) The Attempt at a Solution Pi = xiPi* μi = Gi,m μ = (∂G/∂n) at constant T...
  44. D

    Use moon as generator w earths magnet field

    A moving magnetic field will produce current in a wire. The Earth's magnet field goes beyond the moon. Does that mean bases on the moon could somehow get free energy from a coil setup as it's effectively perpetually moving through Earth's magnetic field?
  45. H

    How do we measure gibbs free energy for irreversible processes?

    I know that gibbs free energy for say a body will be equal to = Gibbs free standard energy at 1M and Ph7(-rtlnkeq) (Where k is the concentration of product/ concentration of reactant at equilibrium)+rtlnk. How can we use the standard gibbs free for irreversible spontaneous processes? Is it...
  46. I

    Did Nikola Tesla discover a way to harness free energy?

    And did he have patent/s for it... I understand that their are a lot of hoaxes and unsourced information out there so I want to know if there is some truth to the claim. I understand that energy can not be created or destroyed but what free energy is referring to is energy that is released...
  47. A

    Free Energy from the Earth's Rotation

    Is it possible to generate energy from the Earth's rotation? Imagine a Foucault Pendulum attached to a dynamo shaft? http://www.google.com/patents/US8299636
  48. microsansfil

    Relevance of Karl J. Friston's Free Energy Principle

    Hello, Does this concept of "Free energy principle ( https://en.wikipedia.org/wiki/Bayesian_approaches_to_brain_function#Free_energy )", developed by Karl J. Friston, showed its relevance ? ie is it a fruitful concept in the field of neuroscience and in biology ? Patrick
  49. J

    Relationship between Free energy change and Equilibrium constant (K)

    1. I have a question regarding the equation ΔG° = -RT lnK. When solving for the equilibrium constant K, what is the relationship between the vapor pressure of each molecular compound in a reaction? ΔG° = Free energy change R = Universal gas constant T = Temperature K = equilibrium...
  50. Greg Bernhardt

    What Is Free Energy: Definition & Equations

    Definition/Summary Free energy is energy available for doing work. Free energy as an independent concept does not really make any sense unless conditions are specified under which the work is to be done, for example: Helmholtz free energy (or Helmholtz energy) A\ =\ U\ - TS is the energy...
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