Re: There's work, and then there's work

[David Rutherford <drutherford@SOFTCOM.NET>]

Bob LaMontagne wrote:
> David Rutherford wrote:
>
> > An analogy might be measuring the amount of water in an elevated tank by
> > measuring the water that flows through a hose attached to the tank after
> > the valve is opened. Imagine that the hose has a hole in the side of it,
> > so that the volume of water flowing out of the hole is exactly equal to
> > the volume flowing out the end of the hose. In analogy with the
> > capacitor experiment, the water flowing out through the side would
> > represent the energy lost to heat dissipation in the calorimeter
> > experiment, and the water flowing out the end would represent the
> > current in the current experiment.
>
> Not really a good analogy - the galvanometer is in series with the resistor in
> the calorimeter.

The water flowing out through the side hole is analogous to the
particles in the environment outside the wire that have picked up energy
from the particles inside the wire. The particles inside the wire have
transferred the part of their energy that's due to the transverse
component of their motion to the particles outside the wire. Therefore,
the calorimeter experiment measures _only_ the part of the energy of the
particles inside the wire that is due to the _transverse_ component of
their velocity. Similarly, the current experiment measures _only_ the
part of the energy of the particles inside the wire that is due to the
_longitudinal_ component of their velocity. The reason that the two
experiments come out with the same result is that, on average, the
transverse and longitudinal components of the velocity are equal.

In order to get the total energy, you need to add the contribution to
the energy from _both_ the transverse _and_ longitudinal components of
the velocities of the particles inside the wire. That means that you
must add together the results from _both_ the calorimeter experiment
_and_ the current experiment to get the total energy stored in the
capacitor.

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555/newtransform.pdf

Applications:
"4/3 Problem Resolution"
http://www.softcom.net/users/der555/elecmass.pdf
"Action-reaction Paradox Resolution"
http://www.softcom.net/users/der555/actreact.pdf
"Energy Density Correction"
http://www.softcom.net/users/der555/enerdens.pdf
"Proposed Quantum Mechanical Connection"
http://www.softcom.net/users/der555/quantum.pdf