What is Free energy: Definition and 302 Discussions

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. codebpr

    A Symmetry breaking in the AdS small/large black hole phase transition

    I am trying to reproduce the results from this paper where they find out the expression for the Landau functional to be $$\psi(x,t,p)=\frac{1}{4}(\frac{1}{x}+6x+px^3-4tx^2)$$ We plot the Landau functional v/s the order parameter($x$) at $p=0.5$ and obtain the Figure 4. from the paper as Now...
  2. aquastor

    Thermodynamics Question Regarding Gibbs Free Energy, Enthalpy, Entropy

    Hello, is someone able to explain why these two are wrong. I am not sure how to figure out the enthalpy direction as the reaction is not changing state of matter, nor is it changing temperature. (Please solve without calculating anything) Thank you
  3. T

    I Rewriting of Gibbs Free Energy in Peksin (Equations 13.35/13.36)

    Hey all, On page 446 in Peskin, he provides 2 different ways of writing the Gibbs Free Energy: $$\textbf{G}(M,t) = M^{1+\delta}h(tM^{-1/\beta})$$, and $$\textbf{G}(M,t) = t^{\beta(1+\delta)}f(Mt^{-\beta})$$ where ##h## and ##f## are some initial condition functions that have a smooth limit as...
  4. P

    Understand Gibbs Free Energy & Activation Energy

    Hi everybody, I don't understand what changes between these two graphs. In particular, why does free energy reach a minimum in one graph and a maximum in the other? Shouldn't a chemical reaction always have an energy maximum, represented by the activation energy?
  5. tbn032

    Chemistry Confusion in relation of Gibbs free energy and equilibrium constant

    SO2(g)+1/2O2(g)⇌SO3(g);ΔHo=-98.32KJ/mole,ΔSo=-95J/(mole-K). find Kp at 298 Kelvin? In given question at first Δ G will be calculated using formula ΔG = Δ H – T x ΔS, by putting the given values in formula we get ΔG = -70.01 kJ/mol. Then Keq will be calculated using equation = Δ G = -RT ln Keq...
  6. T

    I What actually is the free energy? Why is it useful?

    What is the free energy and why is it so important? I realize there's different types but what is the underlying concept? Is a general principle of CM systems to attempt to minimise free energy?
  7. P

    B Can a Planet Made of Glass Generate Free Energy?

    As far as I know, if vacuum antigravitates, it makes the light that travels through it redshift, e.g. in a very large empty box with mirror walls, light will just lose energy. I am interested in the reverse effect, if we had a very large box or planet with mirror walls, that is filled with...
  8. wnvl2

    I Effect of attractive interactions on Gibbs free energy

    Will the presence of attractive interactions between gas molecules raise or lower the molar Gibbs energy of a gas relative to its ‘perfect’ value? I would think that these attracting forces result in a lower energy state. A decrease in the energy state implies a decrease in the enthalpy. A...
  9. B

    Expressions for energy & entropy from free energy (discrete distribution)

    So just by by using the definition of the partition function... $$ Z = \sum_i e^{ \frac {-E_i} {k_BT} } = e^{ \frac {-0} {k_BT} } + e^{ \frac {-\epsilon} {k_BT} } = 1 + e^{ \frac {-\epsilon} {k_BT} } $$ And then, a result we obtained in class by using the Boltzmann H factor to solve for ##S##...
  10. patric44

    Gibbs free energy for superconductor in intermediate state

    hi guys I am trying to derive the Gibbs free energy for a superconductor in the intermediate state , the book(Introduction to Superconductivity by A.C. Rose-Innes) just stated the equation as its : $$ G(Ha) = Vgs(0)+\frac{V\mu_{o}H_{c}}{2n}[H_{a}(2-\frac{H_{a}}{H_{c}})-H_{c}(1-n))] $$ I am not...
  11. GranMix

    Thermodynamic meaning of molar Gibbs free energy

    I know that when it is ΔG>0 , it means there is no spontaneity, when ΔG=0 there is equilibrium, and when ΔG<0, there is spontaneity. But what happens when this is in the context of partial molar properties, when G is molar? I suppose molar ΔG is referred to a solution. Right? In that case, is...
  12. maistral

    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...
  13. RoySRamirez

    Change in Free Energy when Heating a Substance

    Hello everyone! I'm new to the forum, and I've been trying to solve a problem that seems farily but I can't still convince myself of having the right (or wrong) answer. Imagine you warm up one mol of for example potassium hydride from standard temperature 298.15K to 673.15K (400 deg C). It is...
  14. TytoAlba95

    Chemistry MCQ- What is the Gibbs free energy value?

    Where have I gone wrong? According to the key, the right option is a.
  15. P

    I Minimization of free energy in Landau theory

    Thanks in advance for any insight! Following Pathria's discussion of phase transitions, I'm getting tripped up on the discussion of Landau's theory. Pathria begins with a zero-field free energy ##\psi = A/NkT## where ##A## is the Helmholtz free energy. He proceeds to characterize the...
  16. P

    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...
  17. A

    I Why must the Gibbs Free Energy be proportional to N?

    In the textbook Thermal Physics by Daniel Schroeder he says the following: However, I don't follow this argument. Let's say that G was the following: $$G(T, P, N) = (TPN)^{1/3}$$ Then $$G(\lambda T, \lambda P, \lambda N) = \lambda G$$ So $$G$$ is extensive, but $$G \not \propto N.$$
  18. E

    Gibbs free energy problem

    Summary: Please help me with this problem ,I can't do it The normal boiling point of liquid bromine is 58.2°C. At 9.3°C the equilibrium vapor pressure of liquid bromine is 100 torr. From this data, calculate the standard state Gibbs energy of formation of bromine vapor at room temperature...
  19. jaumzaum

    Chemistry Create a Gibbs Free Energy challenge question

    I was thinking about giving the bond energy to calculate the enthalpy change of some exothermic and spontaneous reaction. Than using that exothermic enthalpy to heat the own products and reagents. That would change the Gibbs free energy of the equation (as the elements will be in a different...
  20. sponteous

    Confusion about the use of partial molar Gibbs free energy

    If this belongs in classical physics, please move it there. But it seems like the kind of question chemistry people would know so I'm putting it here. I was reading a textbook on chemical thermodynamics, and it says to raise the partial molar Gibbs free energy of n moles a substance from...
  21. S

    Gibbs Free Energy Equation: why is the entropy change of the system not q/T ?

    What is the entropy change of the system in the Gibbs Free Energy Equation? The general expression for entropy change is ΔS=q/T The only exchange between the system and the surroundings is ΔH done reversibly, with no PV work and no matter transfer, therefore q(syst) = ΔH(syst) therefore surely...
  22. K

    Standard Gibbs free energy equal to zero?

    At equilibrium, we know that deltaG = 0. But what about deltaG_zero, i.e. the standard Gibbs free energy? When is deltaG_zero = 0? In the solution manual it says that it means that K = 1, but by calculating an equilibrium constant you are already stating that we are at equilibrium? I.e. that...
  23. K

    Why is DeltaG Negative for H2O(l) to H2O(g) at Equilibrium?

    Calculate deltaG for the reaction: H2O(l) = H2O(g). 100 degrees celsius, water is clean. P(H2O) = 0.1 bar. Given that it is an equilibrium, I'd think that deltaG would be zero. But the answer is in fact negative. How is that possible?
  24. I

    B Traffic Turbines - Free Energy or Cost Exchange?

    I saw a video on FaceBook today that showed traffic turbines. They supposedly generate "free" energy from the traffic that passes by them causing them to spin. Just because I'm curious, I was wondering if this energy isn't really free, but is in exchange of a minuscule drag put on the passing...
  25. G

    I How Does Helmholtz Free Energy Change During Constant Temperature and Volume?

    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...
  26. MathematicalPhysicist

    Question about Gibbs free energy from Kubos' Thermodynamics

    Advanced Problems textbook. (It's on pages 212-213). I'll post the question and following it the solution in the book: The question: The Solution: What I don't understand is how did they arrive at the identities with ##\frac{\bar{G}_1''-\bar{G}_1'}{0}## and...
  27. W

    I Why is the 'TS term' included in the expression for Gibbs free energy?

    Hello. I'd like to ask a question about meaning of Gibbs free energy. In undergraduate school, I learned that Gibbs free energy is "available" energy we can extract from system at constant pressure and temperature. G=H-TS=U+PV-TS In above expression, however, I can't understand why "TS term" is...
  28. Pushoam

    Free energy per unit volume of an ideal gas

    Homework Statement Homework EquationsThe Attempt at a Solution [/B] I am taking the free energy as the internal energy of the ideal gas. Then the average internal energy per unit volume is ## \frac { 3 nk_B T } {2 } ##. So, the correct option is (c). Is this correct?
  29. VSayantan

    Free Energy of a Simple Quantum System

    Homework Statement [/B]A quantum system has three energy levels, ##-0.12 ~\rm{eV}##, ##-0.20 ~\rm{eV}## and ##-0.44 ~\rm{eV}## respectively. Three electrons are distributed among these three levels. At a temperature of ##1727^o \rm{C}## the system has total energy ##-0.68 ~\rm{eV}##. What is...
  30. W

    Thermodynamics: Free Energy Confusion

    Homework Statement Hi all, I'm having quite a big problem trying to understand the concept of enthalpy and free energy. I feel that a good way to sort this out is to write out what I understand about these things and have people correct me. Thanks in advance for any assistance. I'm learning...
  31. T

    Maxwell Relation, Gibbs Free Energy, Thermal Expansion Coefficient

    Homework Statement By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny. Homework Equations $$G=U-TS+PV$$ $$dG=\mu...
  32. T

    Maxwell Relation, Gibbs Free Energy, Thermal expansion

    By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny. My working:
  33. J

    Calculating Free Energy in Nuclear Fuel Reactions

    Homework Statement Calculate how much free energy in 1kg of nuclear fuel, assuming the most common reaction at a nuclear plant is 235U + n ---> 139Ba + 86Kr + 11n + 176 mev Homework Equations E= mc2 ? 1mol of 235U = 16.5 KJ The Attempt at a Solution Do I need to balance the equation? How...
  34. tze liu

    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
  35. 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...
  36. C

    Gibbs Free Energy -- Connection between V, P, N & T

    Homework Statement For a Particular system the following expression for Gibbs free energy is known: G = -kTN ln (a T^(5/2) / P) where a is a constant (whose dimensions make the argument of the logarithm dimensionless). Obtain expressions for a) The entropy, S b) The connection between V, P...
  37. W

    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...
  38. grandpa2390

    Graphing the Gibbs free energy of mixed gases

    Homework Statement I am needing to graph the Gibbs free energy of mixed gases to determine the range when the gases will form an ideal mixture The two gases have the same Gibbs free energy. Homework Equations ##G = (1-X)G_A + XG_B## for unmixed ##G = (1-X)G_A + (X)G_B + RT(x*ln(x) +...
  39. pallab

    Correct option for n dependence of free energy f per unit

    Homework Statement The equation of state of an ideal gas is p = nkT, where p is the thermodynamic pressure and n = N / V is the thermodynamic variable for the number of particles per unit volume. The n dependence of the free energy f per unit volume of the ideal gas is obtained by the following...
  40. grandpa2390

    Why is the Gibbs Free energy equal to this:

    Homework Statement the isothermal compressibility of graphite is about ##3*10^{-6} bar^{-1}##, while that of diamond is more than ten times less and hence negligible in comparison. (isothermal compressibility is the fractional reduction in volume per unit increase in pressure, as defined in...
  41. Colm

    B If the universe is expanding at an accelerating rate....

    If the universe is expanding at an accelerating rate, either through a "pushing" or "pulling" force in a direction, and we have come from a "big bang point", then I wonder if we could calculate all our vectors at anyone moment and time to find the universal acceleration point and direction. If...
  42. S

    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...
  43. C

    Negative Free Energy - Physical Chemistry

    Homework Statement Hydrogen peroxide can be prepared in several ways. One method is the reaction between hydrogen and oxygen, another method is the reaction between water and oxygen. Given the ΔG°rxn values for each reaction, which method (reaction 1 or 2) requires less energy under standard...
  44. C

    How Do You Calculate ΔG for a Reaction at Non-Standard Conditions?

    Homework Statement For a gaseous reaction, standard conditions are 298 K and a partial pressure of 1 bar for all species. For the reaction 2 NO(gas) + O2(gas) <---> 2 NO2(gas), the standard change in Gibbs free energy (ΔG°) = -72.6 kJ. What is the ΔG for this reaction at 298 K when the partial...
  45. B

    I Including Coulomb interaction in a free energy calculation

    Hi everyone! I am trying to create a crude electron-hopping model to study conductivity in a biological wire composed of discrete sites. The model is pretty simple: imagine a line composed of sites. Electrons can hop from site to site with probabilities that depend on the free energy difference...
  46. Mayan Fung

    Gibbs Free Energy and Enthelpy

    When I studied chemistry in high school, I learned that if the change of enthalpy of a reaction ΔH > 0 , the reaction is endothermic, and if ΔH<0, it is exothermic. However in thermodynamic class, I learnt: $$ ΔG = ΔH - TΔS $$ For a reaction of a battery, the data reads ΔG = -394kJ/mol. (which...
  47. H

    Non-Linear optics vs The 2nd Law of Thermodynamics

    Hi, rank newbie here, with my first post. This one is something I figure every first year student comes up with at some point, but I don't know enough keywords to Search for an answer. (I'm not a student except in the category "of life": this isn't assigned homework) I figger, using a bit of...
  48. doulyftbruh

    Change in Gibbs free energy at equillibrium

    I understand that the change in Gibbs Free Energy at equillibrium is 0 and this leads to the equation -deltaH=TdeltaS. My questions here is that if a reaction is at equillibrium, how can there be any change in enthalpy or entropy at all? Why wouldn't these terms be 0?
  49. E

    Trouble with Gibbs Free Energy & Equilibrium Constant Calc.

    Hello. A known equation that is useful for calculating equilbrium constants is: ΔG° = -RT * ln(K) This is all well and good. Given a standard gibbs free energy of reaction for some given reaction, the equilibrium constant for the reaction can be found. My trouble is in which ΔG° to use. For...
  50. E

    La Chatlier & Gibbs Free Energy Contradiction?

    Say I have an exothermic reaction, whose change in Entropy is positive. (not the most common of reactions, but it can still happen) If I increase the temperature, by La Chatlier's principle, the reaction should move to the left. However, by Gibbs free energy, if I increase the temperature, the...