All Questions
Tagged with differentiation temperature
10
questions
3
votes
1
answer
64
views
Total differential of internal energy $U$ in terms of $p$ and $T$ using first law of thermodynamics in Fermi's Thermodynamics
While reading pages 19-20 of Enrico Fermi's classic introductory text on Thermodynamics, I ran into two sources of confusion with his application of the First Law. Fermi introduces a peculiar notation ...
- 105
-1
votes
3
answers
86
views
Proof that small change in temperature leads to small change in entropy
I have been trying to find a mathematical proof (or even from a reliable source) which verifies that/proves that:
A small change in temperature leads to a small change in entropy.
However, I was ...
1
vote
1
answer
62
views
Weird derivative with respect to inverse temperature identity in Tong's statistical physics lecture notes
While reading David Tong's Statistical Physics lecture notes (https://www.damtp.cam.ac.uk/user/tong/statphys.html) I came across this weird identity in page 26 (at the end of the 1.3.4 free energy ...
- 51
1
vote
1
answer
463
views
Currently self-studying QFT and The Standard Model by Schwartz and I'm stuck at equation 1.5 in Part 1 regarding black-body radiation
So basically the equation is basically a derivation of Planck's radiation law and I can't somehow find any resources as to how he derived it by adding a derivative inside. Planck says that each mode ...
2
votes
0
answers
83
views
Is my geometric interpretation of $T \left(\frac{\partial S}{\partial T}\right)_P = \left(\frac{\delta Q}{dT}\right)_P$ correct?
I originally started writing this as just a question, but in the process of writing it I may have solved it myself. Still, I would very much appreciate if someone more knowledgeable than myself took a ...
- 1,215
2
votes
3
answers
152
views
Temperature and entropy
One could define temperature as follows:
$$T^{-1} = \left(\frac{\partial S}{\partial U}\right)_{N,V}$$
I was reading Schröder, and he says that we can define temperature in another way:
$$T = \left(\...
- 23
0
votes
0
answers
281
views
Partial derivatives in thermodynamics
In thermodynamics many definition has been made from partial derivatives at constant conditions for instance:
Let U be U:$f(S,V,m_k)$ then:
$$T = \left( \frac{\partial U}{\partial S} \right)_{V, m_{...
0
votes
2
answers
282
views
Regarding directional derivatives [closed]
we know directional derivatives are the rate of change of any given scalar field along the given direction, and it is also equal to scalar product of gradient of the field and the unit vector along ...
- 13
1
vote
1
answer
5k
views
What's the meaning for the derivatives for temperature and pressure?
If we view the temperature and pressure as the function of time and space,
$$T = T(x,y,z,t) \quad ; \quad P = P(x,y,z,t)$$
then what's the meaning for the following derivatives?
$$\nabla T \...
- 1,757
7
votes
6
answers
8k
views
How is gradient the maximum rate of change of a function?
Recently I read a book which described about gradient. It says
$${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r},$$
and suddenly they concluded that $\nabla T$ is the maximum rate of change of $f(T)$ ...
- 872