All Questions
Tagged with differentiation energy
28
questions
3
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1
answer
64
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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
0
votes
3
answers
112
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Deduction of Kinetic energy operator in quantum mechanics
In Chapters 1 and 2 of Introduction to Quantum Mechanics Third edition, Griffiths and Schroeter state that to get kinetic energy operator one replaces momentum with $p\rightarrow -i\hbar\,\partial/\...
2
votes
1
answer
109
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Sum of two state functions is not path independent
I am trying to explain the different physical meanings of the various thermodynamic potentials (before resorting to Legendre transforms, and without making appeals to statistical mechanics) and I ...
- 195
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2
answers
63
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How do extreme points work in Statistical Mechanics?
Suppose that I have an $S,V,N$ ensemble. Every variable is a function of the other variable: $U(S,V,N)$, $S(U,V,N)$, $V(S,U,N)$ and $N(S,U,V)$. The functions are everywhere differentiable. But there ...
- 1,440
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3
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432
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Goldstein: derivation of work-energy theorem
I am reading "Classical Mechanics-Third Edition; Herbert Goldstein, Charles P. Poole, John L. Safko" and in the first chapter I came across the work-energy theorem (paraphrased) as follows:
...
- 232
1
vote
1
answer
463
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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 ...
0
votes
0
answers
51
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Can we define $\text dW$? [duplicate]
I am currently taking applied thermodynamics at my university, and for the definition of entropy this is the formula used in the book (Thermodynamic for Engineers by Moran, Shapiro, Boettner, Bailey): ...
0
votes
0
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126
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Work-Energy Principle Derivation
I am currently in Mechanics I and both my professor and my book have derived the work principle in this way and I even asked about its derivation during class, but it has me puzzled.
I don't ...
1
vote
1
answer
161
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$dT/dx=0$ always true?
In a Classical Mechanics book I found the assumption that for an arbitrary particle with constant mass in the Real line $dT/dx=0$, with T the Kinetic Energy i.e. $T=(m·\dot x^2)/2$
My hypothesis is ...
- 145
2
votes
3
answers
152
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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:
$$T = \left(\...
- 23
0
votes
1
answer
51
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How do I show that $\dfrac{dE}{dt} = \dfrac{\partial U}{\partial t}$ where $U(\mathbf{r}_1,...,\mathbf{r}_N,t)$ is the potential energy?
I'm working through Chapter 1 of Analytical Mechanics for Relativity and Quantum Mechanics, and in Section 1.8, they derive the equality in the question. To show this, they claim that
$$\dfrac{dT}{dt} ...
3
votes
1
answer
602
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Physical interpretation of total derivative
Can I get some help interpreting the following?
"Since this is a total differential (that is, it only depends on the final state, not how the particle got there), we can integrate it and call ...
- 1,031
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votes
0
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44
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How to see that kinetic energy depends on generalised coor., gen. vel. and time?
Let $u_{ik}$ denote the $i^{th}$ component of the position vector of the $k^{th}$ particle. Then kinetic energy of the system of $N$ particles is given by:
$$T=\frac{1}{2}\sum^N_{k=1}\sum^3_{i=1}m_k\...
- 192
0
votes
1
answer
293
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Computing total derivative of Kinetic Energy w.r.t time
I am confused as to how to take the total derivative $\frac{dKE}{dt}$, where $KE$ is the kinetic energy.
I know that $KE = 1/2 *m * \dot{\vec r} \cdot \dot{\vec r}$. From here, if I take derivative ...
- 111
2
votes
1
answer
99
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Work-Kinetic energy theorem derivation
So I came across this derivation in the book Classical Mechanics by Herbert Goldstein. I don't follow from the second step onwards. I understand that there's a dot product, but how do you compute it? ...
- 87