Recent content by TSny

I'm not familiar with any treatments of thermodynamics that prove differentiability of ##U##. I think physicists tend not to worry too much about it. They just assume differentiability. For example, regarding entropy, Callen gives on page 28: So, Callen postulates differentiability of ##S##.

Even though we need quantum mechanics to describe atoms, we still assume that systems of atoms have well-defined energies and that the law of conservation of energy is valid. On page 17 of Callen, we read When work is done on an adiabatically enclosed system, we can imagine it being performed...

I think Callen’s conclusion follows from his discussions earlier in Chapter 1. The change in the internal energy of a system during a process equals the net amount of energy transferred to the system during the process. This follows from the principle of conservation of energy. For simple...

You can read a discription for the chart here. Click on the picture and zoom in.

I don't know. A highly reflective metal surface or mirror would not absorb very much. Each ray of light in the beam obeys the law of reflection at the curved surface.

You might experiment with fanning out the beam by reflecting off a smooth cylindrical surface. Here, I used a ceramic mug.

Very good. I'm glad I could help.

Your result ##-\frac 1 2 \lambda v^3## is correct for the rate at which KE is lost to heat at point B. I’m not sure of your thought process in going from ##\Delta KE = - \frac 1 2 \lambda \Delta x v^3## to the result for the rate ##\frac{dKE}{dt}##. But it might be fine. I was just trying to...

Yes Rigidity imposes a condition on the velocities of two points of the rod, not the accelerations.

Good. Ok. This is less of an eyesore if you write it as ##U = U_0 -\lambda ghx##, where ##U_0## is the total potential energy at the moment of release (##x = 0##). The force that the table exerts on the chain does not do any mechanical work since the force doesn't move the chain through any...

As pointed out by @Steve4Physics, mechanical energy is not conserved. However, you can still solve it using energy concepts. (1) Find an expression for the KE of the chain at the instant the upper end of the chain has moved a distance ##x## from point ##A##. Express in terms of ##\lambda##...

Yes, they correctly accounted for gravity. But, they did not account for the change in chemical energy ##U_{chem}## of the battery. Their solution predicts an imaginary value for the final speed of the plate for the case where ##g = 0.## This is a good problem for demonstrating the importance...

Your two methods look correct. I did catch a spot where you have two compensating errors: Check the signs in this calculation. However, your result of ##\frac 1 d## is correct. To see that their answer can't be correct, suppose the experiment is done in zero gravity.

Yes. Nice analogy.

Good. If you wish, you can post your work for ##\nabla \mu## and we can review it.