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Questions tagged [maxwell-relations]

Maxwell relations are equalities involving the mixed second partial derivatives of thermodynamic potentials.

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Thermodynamics partial derivative brackets

Today I half-remembered a wonderful trick to doing thermodynamical partial derivatives, but I neither recall the full set of rules, nor where I got them from! I was hoping someone else knows where they come from or where I can find them written…
F. Bardamu
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Multivariable calculus and Thermodynamics

Somewhere in my thermodynamics text I read the following. $\left(\frac{dU}{dP}\right)_{V} = \left(\frac{\partial U}{\partial T}\right)_{V} \left(\frac{\partial T}{\partial P}\right)_{V}$ Is it correct? It should be something like…
The Imp
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Any difference between thermodynamic double-derivative and derivative "at constant" value?

Reading about the Maxwell relations has left me confused, and I want a basic sanity check regarding the notation. The Wikipedia article breezes over the following switch of notation without really describing it: $$ \left(\frac{\partial T}{\partial…
Alan Rominger
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Fundamental thermodynamic relation: derivation of "non-natural" variables

Maybe this could be case where a question, other than an answer, could be wrong, but whatever... Let's start with the fundamental thermodynamic relation in differential form for a hydrostatic system, $dE=TdS-PdV+\mu dN$. Via the Euler's homogeneous…
Lo Scrondo
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Does the temperature of a real gas decrease in the adiabatic free expansion?

The internal energy $U$ of a given mass of a real gas can be regarded as a function of temperature and volume i.e., $U(T,V)$. Under adiabatic free expansion, the change in the internal energy is zero because $\delta Q=0$. The workdone $\delta W=0$…
SRS
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How many Maxwell relations are there in thermodynamics?

I am just learning about partial differentiation and Maxwell relations cropped up as an example. Considering that we are dealing with the 4 different variables $p$, $V$, $S$ and $T$. I would think that there would be 6 Maxwell relations because when…
Meep
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Finding Maxwell relations

I feel I am missing something about deriving Maxwell relations. I have read http://ocw.mit.edu/courses/physics/8-044-statistical-physics-i-spring-2013/readings-notes-slides/MIT8_044S13_notes.Max.pdf and as far as I can see if we have $dE=TdS+FdL$,…
Trajan
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Are Maxwell Relations valid only out of saturation?

My thermodynamics book suggests that the Maxwell Relations must be used when dealing with a single-phase system. The equations come right after the section Mathematical Relations for the Homogeneous Phase, in which the following is stated: In the…
André Chalella
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Calculating inner energy, understanding maxwell relations

I have $n$ mole of an ideal gas with pressure $p$, volume $V$, temperature $T$ and constant heat capacity $C_v$. The question is to calculate the inner energy $U$. Solution: $$ \left( \frac {\partial U}{\partial T} \right)_V=C_v \to U(T,V)=\left(…
armara
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Cross-differentiation to derive the maxwell relation $\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V$

How can I use $T=\left(\frac{\partial E}{\partial S}\right)_V$ and $P=-\left(\frac{\partial E}{\partial V}\right)_S$ to derive $$\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V$$ The book (Statistical…
whatwhatwhat
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Temperature change in Adiabatic stretching of liquid film

The first law applied to a liquid film is $dU = dQ +2\sigma dA$ where $\sigma$ stands for surface tension. Or $dQ = dU + (-2\sigma) dA \leftrightarrow dQ = dU + PdV$ Now suppose we wish to find what happens to temperature if I increase the area…
The Imp
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Find an expression for S(T,x) from tension and specific heat

I'm working on a problem from a Statistical Mechanics lecture series online, and on the homework, I hit a bump in this problem. Here is the problem set, and I'm asking about #1.c. Short version, we are given that the force to move the filament is…
JoDraX
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Using Maxwell's demon alongside quantum mechanics to contradict 2nd law of thermodynamics

Suppose we have a steady state universe with a gas chamber resembling that of Maxwell's demon that is used to power this hypothetical heat engine as molecules transfer to their respectable sides based on temperature. Now, suppose we ran this machine…
user1939991
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In thermodynamic identity, dU=TdS-PdV. Are dS and dV orthogonal or is (T,P) defined in a conjugated space from (dS,dV)?

In thermodynamic identity, we say dU=TdS-pdV, and only Maxwell's relation is required for U to be a proper behaved thermodynamics variable. But from multivariable calculus, that result requires dS and dV to be orthogonal to each other. And I never…
Chong
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Using Jacobians to prove an identity

I have to prove the identity $$ \left(\frac{\partial U}{\partial V}\right)_T=T\left(\frac{\partial p}{\partial T}\right)_V-p $$ I know how to do this using Maxwell's relations, but the assignment specified that I have to use Jacobian…
user44502
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