Living Force and Heat

Living Force and Heat
Joule believed that water at the bottom of a waterfall should be slightly warmer
than water at the top, and he made attempts to detect such effects (even on his
honeymoon in Switzerland, according to an apocryphal, or at any rate embellished,
story told by Thomson). For Joule this was an example of the conservation
principle that “heat, living force, and attraction through space . . . are mutually
convertible into one another. In these conversions nothing is ever lost.” This
statement is almost an expression of the conservation of mechanical and thermal
energy, but it requires some translation and elaboration.
Newtonian mechanics implies that mechanical energy has a “potential” and a
“kinetic” aspect, which are linked in a fundamental way. “Potential energy” is
evident in a weight held above the ground. The weight has energy because work
was required to raise it, and the workcan be completely recovered by letting the
weight fall very slowly and drive machinery that has no frictional losses. As one
might expect, the weight’s potential energy is proportional to its mass and to its
height above the ground: if it starts at a height of 100 feet it can do twice as
much workas it can if it starts at 50 feet.
If one lets the weight fall freely, so that it is no longer tied to machinery, it does no work, but it accelerates and acquires “kinetic energy” from its increasing
speed. Kinetic energy, like potential energy, can be converted to work with the
right kind of machinery, and it is also proportional to the mass of the weight. Its
relationship to speed, however, as dictated by Newton’s second law of motion,
is to the square of the speed.
In free fall, the weight has a mechanical energy equal to the sum of the kinetic
and potential energies,
mechanical energy kinetic energy potential energy. (1)
As it approaches the ground the freely falling weight loses potential energy, and
at the same time, as it accelerates, it gains kinetic energy. Newton’s second law
informs us that the two changes are exactly compensating, and that the total
mechanical energy is conserved, if we define
mv2
kinetic energy (2)
2
potential energy mgz. (3)
In equations (2) and (3), m is the mass of the weight, v its speed, z its distance
above the ground, and g the constant identified above as the gravitational acceleration.
If we represent the total mechanical energy as E, equation (1) becomes
mv2
E mgz, (4)
2
and the conservation law justified by Newton’s second law guarantees that E is
always constant. This is a conversion process, of potential energy to kinetic energy,
as illustrated in figure 5.2. In the figure, before the weight starts falling it
has 10 units of potential energy and no kinetic energy. When it has fallen halfway
to the ground, it has 5 units of both potential and kinetic energy, and in the
instant before it hits the ground it has no potential energy and 10 units of kinetic
energy. At all times its total mechanical energy is 10 units.
Joule’s term “living force” (or vis viva in Latin) denotes mv2, almost the samething as the kinetic energy , and his phrase “attraction through space” means
mv2
2
the same thing as potential energy. So Joule’s assertions that living force and
attraction through space are interconvertible and that nothing is lost in the conversion
are comparable to the Newtonian conservation of mechanical energy.
Water at the top of the falls has potential energy only, and just before it lands in
a pool at the bottom of the falls, it has kinetic energy only. An instant later the
water is sitting quietly in the pool, and according to Joule’s principle, with the
third conserved quantity, heat, included, the water is warmer because its mechanical
energy has been converted to heat. Joule never succeeded in confirming
this waterfall effect. The largest waterfall is not expected to produce a temperature
change of more than a tenth of a degree. Not even Joule could detect that
on the side of a mountain.
Joule’s mechanical view of heat led him to believe further that in the conversion
of the motion of an object to heat, the motion is not really lost because heat
is itself the result of motion. He saw heat as the internal, random motion of the
constituent particles of matter. This general idea had a long history, going back
at least to Robert Boyle and Daniel Bernoulli in the seventeenth century.
Joule pictured the particles of matter as atoms surrounded by rapidly rotating
“atmospheres of electricity.” The centrifugal force of the atmospheres caused a
gas to expand when its pressure was decreased or its temperature increased.
Mechanical energy converted to heat became rotational motion of the atomic
atmospheres. These speculations of Joule’s markthe beginning of the development
of what would later be called the “molecular (or kinetic) theory of gases.”
Following Joule, definitive workin this field was done by Clausius, Maxwell,
and Boltzmann.