Linked Questions
10 questions linked to/from Physical interpretation of total derivative
2
votes
4
answers
793
views
Why do we use different differential notation for heat and work?
Just recently started studying Thermodynamics, and I am confused by something we were told, I understand we use the inexact differential notation because work and heat are not state functions, but we ...
- 283
4
votes
2
answers
510
views
Converting differential to gradient
Landau & Lifschitz's fluid mechanics book proposes the following statement for an isentropic proccess:
$$dH=vdp \Rightarrow \nabla H=v\nabla p$$
What's the rigorous way to get this result (...
- 43
3
votes
3
answers
241
views
Does $\int{\frac{1}{dx}}$ have any meaning in physics?
Recently I came across this problem :
There are two identical parallel plates of length $L$ and breadth $B$ on the XZ plane . One plate passes through $Y = 0$ and the other passes through $Y = d$. ...
- 876
5
votes
2
answers
462
views
How does one interpret thermodynamic differentials?
Why do we treat thermodynamic quantities mainly with differential? What is the intuitive reason behind it.
In sense, what is the right perspective to look at these things from? It is quite different ...
- 8,040
0
votes
1
answer
379
views
Derivative of the osmotic pressure with respect to the chemical potential via Gibbs-Duhem
So I was reading through Atkins "Physical chemistry" 10th edition and was wondering something. Suppose you have an athermal system of $k$ particles, let us define the Gibbs-Duhem equation ...
- 3
0
votes
2
answers
315
views
Thermodynamic equilibrium state of constant $(p,S)$ system
The internal energy as a function of its natural variables is:
$$dU=-p dV+TdS$$
where $p$ is the system pressure and $dS$ includes only changes of the entropy due to heat transfer (the "...
- 474
1
vote
2
answers
120
views
Differential form of Planck's Distribution Law interpretation
So I didn't encounter differentials that often until now, I was taught that the seperate parts of $dy/dx$ for example are not supposed to have any sort of independent existence - ok.
(Calculus, 4th ...
- 153
0
votes
1
answer
102
views
Confusion regarding the definition of electrochemical potential
I am having trouble understanding the concept of the electrochemical potential $\mu$. In my textbook the electrochemical potential is defined as $\mu=\frac{\partial G}{\partial n}$. It seems to me as ...
- 331
1
vote
0
answers
62
views
A trick for derivatives of thermodynamic quantities [closed]
Starting from
$$dU=TdS-PdV$$
We can write, for instance $U(T,V)$ and $S(T,V)$ to obtain:
$$\left(\frac{\partial U}{\partial T}\right)_VdT+\left(\frac{\partial U}{\partial V}\right)_T dV=T\left(\frac{\...
- 225
0
votes
1
answer
47
views
Why is the force being the differential of a potential equivalent to it being a conservative force?
I was reading Goldstein's book on mechanics and came across this theorem:
$F(r) = - \nabla V(r)$ is a necessary and sufficient condition of the force field being conservative.
So far, I have ...
- 169