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.
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?
I'm studying Thermodynamics and I'm a little stuck at this problem.
1. Homework Statement
Starting with the first Maxwell relation, derive the remaining three by using only the relations:
$$\left(\frac{\partial x}{\partial y}\right) _{z} \left(\frac{\partial y}{\partial z}\right) _{x}...
Homework Statement
Given the entropy of a system :
$$ 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$$
to find the mathematical constraint of α and β
Homework Equations
dU = TdS - PdV + μdN
The...
Homework Statement
This is question 2.18 from Bowley and Sanchez, "Introductory Statistical Mechanics" .
Show with the help of Maxwell's Relations that
$$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...
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...
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...
I'm learning about Maxwell relations of Thermodynamics, but it's difficult for me to find more books about this in Vietnamese. So, I want to ask you about some english ebook about this. Thanks a lot!
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...