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"I would never die for my beliefs because I might be wrong."

-- Bertrand Russell


Jul
6
revised Time to immerse in a fluid
edited body
Jul
6
comment Time to immerse in a fluid
@udiboy: I think the sphere is somewhat harder but more realistic. With the other forms, I would have to make an additional assumption of how the piece drops into the fluid to be able to compute things. With the sphere, it obviously doesn't matter.
Jul
6
comment Time to immerse in a fluid
@udiboy: Yes, but as you can see, calculus is unavoidable. The final formula, whatever the method you use to arrive at it will contain an integral. Of course, you could maybe partly guess a simplified formula by some dimensional analysis I suppose.
Jul
6
revised Time to immerse in a fluid
added 867 characters in body
Jul
6
answered Time to immerse in a fluid
Jun
13
comment Ascertaining a mathematical equality to derive a partition function
I've made some edits. But it now seems to me your expression is trivially true.
Jun
13
revised Ascertaining a mathematical equality to derive a partition function
edited body
Jun
13
comment Ascertaining a mathematical equality to derive a partition function
The second part about $\mathcal{N}(x)$ doesn't make sense. What is $n$, where does it come from?
Jun
11
comment The Hamiltonian for clocks?
@freude: I am from Leuven. Maybe we can carry this on in a chatroom?
Jun
11
comment The Hamiltonian for clocks?
I'm not sure what you're talking about. $U=e^{i\omega t}$ is just fine, it has period $T=2\pi/\omega$. It's unitary and therefore associated to the Hermitian operator $H=\omega$.
Jun
10
comment Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
@Nathaniel: I suppose you're right. It seems to even be an open problem to understand when Fourier's law applies. I in fact even know that it is an open problem to find derivations of Fourier's law from microscopic principles in cases where it does apply.
Jun
9
revised Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
added 463 characters in body
Jun
5
comment Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
I'm sorry, but what you say doesn't make any sense. I suggest you follow a course on vector calculus before attempting to read about thermodynamics in this book. You are very confused. There are some good Schaum series books on vector calculus. Look for them, they are quite cheap.
Jun
5
comment Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
No, temperature gradient also has three directions, that's equation (2-4). You are confused because you don't see that $Q$ and $T$ can be scalars, while their derivatives $\vec{q}$ and $\nabla T$ are vectors.
Jun
5
comment Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
It means that heat can flow in three directions. Through the x-side of the box, through the y-side or through the z-side, hence why we can speak of a heat flux vector.
Jun
5
comment Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
I don't see any equation (2-3) on page 65.
Jun
5
comment When we talk about speeds in relativity theory, where are they measured?
With respect to what are you measuring your velocity and the Earth's velocity? I think you still don't quite get it. Your question and assertions make no sense because you never define your reference system. Velocity is relative to a reference system.
Jun
4
revised Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
added 210 characters in body
Jun
4
comment Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
Your link doesn't seem to work.
Jun
4
comment Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
It is not the original form of the law. But while vector calculus didn't exist in Fourier's time, Fourier was well aware that heat fluxes could flow through any side of my hypothetical box I was talking earlier. He would have had a $dQ/dt$ for each side, hence a vector.