Re: first law of thermo

["Carl E. Mungan" <mungan@USNA.EDU>]

> What about the Rumford experiment, for example?  If
> you want it to be numerical (as well as conceptual),
> let a cannon with heat capacity C rotate through an
> angle theta while subject to a torque tau;  your
> mission, should you decide to accept it, is to
> calculate delta T.

I'm a bit mystified. Perhaps part of this is because I haven't read
the Rumford citation you have on your webpage (but it's on my "to
read" list).

But this is not conceptually different than kinetic friction of a
block sliding to rest on a table, right? If so, here's how I see
things:

(a) Suppose I put both the block and table (cannon and boring tool)
in the system in Step 2 below. Further, I assume C = m1*c1 + m2*c2
(where m = mass and c = specific heat capacity of each object in the
system).

(b) In the first step, I calculate work on the block as -friction *
linear displacement. I do not claim this to be thermodynamic work;
call it center-of-mass work if you feel a distinguishing adjective is
necessary. But for simplicity and consistency with mechanics books,
label it W. In the second and third steps, I claim that a standard
chain of reasoning (see below) shows W = C * delta T. I would not
invoke Q for the system of block + table. (If the system is the block
alone, things are not so simple and we need to consider the timescale
for thermal equilibration and possible subsequent
conduction/radiation to the air, to cool parts of the borer or table,
etc.)

(c) I would certainly claim W also equals delta K for the block.

To me, all of this is standard stuff, basically what any textbook
would do. If you insist on the cannon boring problem, I can put
together a similar line of reasoning for it. But I believe the basic
ideas are here. If you have a different solution to this problem, I'm
all ears.

** Details of the chain of reasoning **

Step 1. LOOK IN MECHANICS CHAPTER
Apply work-kinetic-energy theorem to block AS A WHOLE => -umgx = -m*v0^2/2.

Step 2. LOOK IN CONSERVATION OF ENERGY CHAPTER
Apply delta(E) = 0 assuming an isolated block+table system => 0 =
-m*v0^2/2 + delta E_int. Note that I have *not* invoked any
thermodynamics so far.

Step 3. LOOK IN THERMODYNAMICS CHAPTER
Apply definition of heat capacity C = delta E_int / delta T.
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/