Re: CONSERVATION OF ENERGY

[Leigh Palmer <palmer@sfu.ca>]

> Something must be wrong somewhere; my immediate reply to what Leigh wrote
> did not come to me. I suspect it was lost. So let me answer again in a
> slightly different form:

I thought I'd answered this in the earlier for, and those answers still
apply. Ludwik has now qualified c (as I suggested) and a further answer
is appropriate.

> ***********************************************************************
>                              On Sun, 13 Ludwik asked:
>
> > > Leigh, how should dU=c*m*dt be called? We used to call it "heat" but
> > > this was in conflict with how heat is defined in thermodynamics. What
> > > is wrong with the name "thermal energy"? It is now used by many authors.
>
>                              The answer from Leigh was:
>
> > As you state, it should properly be called heat, since a process, though
> > not a uniquely specified one, is implicit. It is certainly not an energy.
> > Use of the symbol dU (by which I infer you mean the change in U) is most
> > improper; heat is not the change in anything. You should use Q instead:
> >
> >                              Q = m c dT
> >
> > where m is the mass of a homogeneous system having heat capacity per
> > unit mass c (some modifier is appropriate here) and dt is the change in
> > temperature that occurs in the process of heating.
>
> Please note that c refers to a constant (zero) external pressure (vacuum).
> No mass is lost and T is a state variable. Thus the product m*c*dT is
> path independent. Following numerous authors I do not want to call this
> quantity heat; a concept defined when we teach thermodynamics. Is it not
> true that the accepted definition states that "heat is that part of internal
> energy which is transfered through a system boundary due to a difference
> of temperatures"?

That definition makes the first law of thermodynamics redundant. There
should be no mention of internal energy in the definition of heat.

> In the example used, dQ is due to friction, it is not
> a difference of temperature responsible for the "injection of random
> energy into the system".

There is no heat involved in the problem you stated. The transfer of
energy that occurs is, in the equilibrium thermodynamic limit (where
the system evolves sufficienly slowly that it is never far from a
state of thermodynamic equilibrium), classified as work. So far as
my education has extended I have never been introduced to "random
energy". I think it is a concept which is not needed; classical
thermodynamics does nicely without it.

> If I am correct (that c*m*dT is not heat, as defined in thermodynamics)
> then what name should be given to it? How can we teach without having
> distinct names for distinct physical quantities? You can invent another
> situation in which the cube (from our example) does not slide at all and
> dT is a result of an electric current (chemical reactions in a nearby
> battery). Or a radioactive iron isotope may be responsible for a slight
> increase in temperature. These are different paths leading to the same
> outcome. Let me repeat the original question; What is wrong with the name
> "thermal energy"? I did not invent it.

You have now qualified c to be the heat capacity per unit mass at
zero constant pressure. I take it m is the mass of your sliding cube,
and dT is the temperature increase resulting from the process. Then
m*c*dT is equal to the change in the internal energy of the block in
this process. Note that I say it is equal to the change, not that it
*is* the change. The equality arises because of a concept called the
mechanical equivalent of heat. This change in internal energy is the
same as would have been achieved through heating the block through
the came temperature difference at zero pressure *or* doing an equal
amount of work W = m*c*dT on it. In the latter case the change in
the internal energy would be equal to W.

The name "thermal energy" is unnecessary, and it is misleading. The
implication is that the energy has somehow been acquired from a
source which was used to heat the system. The terms work, heat, and
internal energy, on the other hand, are well defined and are not
misleading. Moreover they seem to be sufficient to the task.

Leigh