Temperature in Thompon's experiments.

[elephantorz]

1. In one of Thompson's experiments he placed a thin metal foil in the electron beam and measured its temperature rise. Consider a cathode-ray tube in which electrons are accelerated through a 2,000 V potential difference, then strike a 10 mg copper foil.

• How many electrons strike the foil in 10 s, if the foil temperature rises 6.0 C?

2. r = (mv)/(qB)
v = E/B




3. I am really kind of at a loss as to how to set up this...I am not sure I am in the right track, and I don't know if there is an equation that relates temperature with electricity, I am sure there is and if there is I would like to be pointed to it, I think that's really all I need, unless I am completely doing the wrong thing :/

Thanks guys (that includes females :] ).

 

[alphysicist]

Hi elephantorz,

Here are a couple of points that might help:

What will being accelerated through 2000 V do to the electrons?

The temperature rise of this copper must be coming from an energy transfer to the copper. Where and in what form was this energy beforehand?

 

[elephantorz]

I asked my teacher about this, she pulled out an E$$_{th}$$= mc$$\Delta$$T, I remembered this vaguely from Physics I [calc-based], I went back to look at the equation sheet and it seems this included W, I am assuming this is work.

For one, what does the th stand for? I never took this class with her, since I am doing independent study, I took Physics I about...um, maybe 5 yrs ago? So I have a bunch of theoretical questions and just some details like that [I got the answer to the problem but I want to know where it comes from].

But the equation is really ΔE = Q + W, am I to assume there is no work being done? Since it's being accelerated over a distance or ?

Also, I went another way with this, I was trying to find the resistivity of the metal as a function of time, so $$\rho$$(T) = $$\rho$$$$_{0}$$[1 + $$\alpha$$[T-T$$_{0}$$]]

Could I have potentially done it that way? Or would I have just failed due to lack of information?

I know these are a lot of questions, I'm sorry, the answer though is :

7.218 x 10^(13) electrons.​

I also have a question there, she divides the E$$_{th}$$ by the Kinetic Energy, I reasoned that maybe this is because the heat created has been transformed into moving energy, but I am not too confident with this reasoning.​

Again, thanks!

EDIT: Also, LaTex seems to be having issues with subscript, the th and the 0 are really subscripts.

 

[alphysicist]

The formula $$E^{\rm th}=mc\Delta T$$ gives the temperature rise of the material if you know the energy transferred.

That energy has to be coming from the electrons. Can you calculate their energy before they collided with the copper?