# What is Maxwell relations: Definition and 18 Discussions

Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell.

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1. ### Partial derivatives of enthelpy and Maxwell relations

I've attached images showing my progress. I have used Maxwell relations and the definitions of ##\alpha##, ##\kappa## and ##c##, but I don't know how to continue. Can you help me?

4. ### Problems related to Maxwell relations

Homework Statement Given the entropy of a system : $$S = AU^αV^βN^{1-α-β}$$ The problem requires me to write $$(\frac{∂T}{∂U})_{V,N} > 0, (\frac{∂P}{∂V})_{U,N} < 0, (\frac{∂μ}{∂N})_{U,V} > 0$$ to find the mathematical constraint of α and β Homework Equations dU = TdS - PdV + μdN The...
5. ### Application of Maxwell's Relations

Homework Statement This is question 2.18 from Bowley and Sanchez, "Introductory Statistical Mechanics" . Show with the help of Maxwell's Relations that $$T dS = C_v dT + T (\frac{\partial P}{\partial T})_V dV$$ and $$TdS = C_p dT - T( \frac{\partial V}{\partial T})_P dP.$$ Then, prove that...
6. ### Show that (du/dv)t=T(dp/dT)v-p - please explain

Homework Statement Show that (du/dv)T = T(dp/dt)v - p Homework Equations Using Tds = du + pdv and a Maxwell relation The Attempt at a Solution I've solved the problem, but I'm not entirely sure my method is correct. Tds = du + pdv ---> du = Tds - Pdv - Using dF=(dF/dx)ydx +(dF/dy)xdy...
7. ### 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...

9. ### Thermodynamics - Maxwell Relations

Homework Statement 2. The attempt at a solution I've tried using the relation Cp = T(dS/dT), isolating "T" for T = Cv2(dT/dS) and using the maxwell relations to reduce the derivatives, reaching, T = Cv2/D (dV/dS), but i don't think this is the right way to do solve this problem, i couldn't...
10. ### Maxwell relations Thermodynamics

Homework Statement Show that: (\frac{∂T} {∂V})_S,_n=-(\frac {∂P} {∂S})_V,_n Homework Equations dU=TdS-PdV+μdn The Attempt at a Solution \frac {∂} {∂S} (\frac{∂U} {∂V})_S,_n=-(\frac {∂P} {∂S})_V,_n \frac {∂} {∂V} (\frac{∂U} {∂S})_V,_n=(\frac{∂T} {∂V})_S,_n I tried to isolate T and P...
11. ### Maxwell Relations: when are they valid?

Hi, I have a question If I am not mistaken, the Maxwell relations of theromdynamics -----for example: ∂G/∂T) = -S ; ∂G/∂P) = V ----- are valid only for reversible processes. On the other hand, dG = ∂G/∂T)*dT + ∂G/∂P)*dP + ∑ μi dni is valid for any process. This means that dG = -SdT + VdP...
12. ### How to obtain maxwell relations

Hey, I have had a lot of trouble understanding how one obtains a Maxwell relation. So let's say in general I know(from a specific problem) T ds = dE - F dL where F is a tension and L is a length, E is the energy T is the temperature and S is the entropy of a system. In a specific...
13. ### Maxwell Relations: Derivations for Enthalpy and Entropy

Maxwell Relations - derivations Homework Statement 1. Derive the Maxwell Relation based on the enthalpy. 2. Derive the Maxwell Relation based on the entropy. Homework Equations H=U+PV dU=dq+dw dw=-PdV dS=dq/T The Attempt at a Solution 1. I feel like I've gotten this one, but...
14. ### Partial derivatives (Maxwell relations) in thermodynamics

My professor did this in lecture, and I can't figure out his logic. Can someone fill in the gaps? He went from: dS = \left( \frac{\partial S}{\partial P} \right)_T dP + \left( \frac{\partial S}{\partial T} \right)_P dT (which I totally understand; it just follows from the fact that...
15. ### Where Does the Entropy Formula Come From in Thermodynamics?

Hey guys. Right, I have been studying the Maxwell thermodynaic relations. But I have come across entropy as dS = (bS/bT)_P(dT) + (bS/bP)_T(dP) where b is the partial differential symbol. I don't understand where this comes from, which suggests S(T,P). I can't find a derivation of...
16. ### Maxwell relations with heat capacity.

Maxwell relations with heat capacity. Solved. 1. Homework Statement Use the Maxwell relations and the Euler chain relation to express (ds/dt)p in terms of the heat capacity Cv = (du/dt)v. The expansion coefficient alpha = 1/v (dv/dt)p, and the isothermal compressibility Kt = -1/v (dV/dp)T...
17. ### Maxwell relations with heat capacity

Homework Statement Use the Maxwell relations and the Euler chain relation to express (ds/dt)p in terms of the heat capacity Cv = (du/dt)v. The expansion coefficient alpha = 1/v (dv/dt)p, and the isothermal compressibility Kt = -1/v (dV/dp)T. Hint. Assume that S= S(p,V) Homework Equations...
18. ### Maxwell Relations (not equations)

I just recently learned the Maxwell Relations in Thermodynamics. We aren't really doing anything with them, just went through the derivations. In deriving them, we started with the equation of state: TdS=dU+PdV where T is temperature, S entropy, U internal energy, P pressure, V volume. We...