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Ideal Gas Thermodynamics: Specific Heats, Isotherms,
Adiabats
Michael Fowler 7/15/08
Introduction: the Ideal Gas Model, Heat, Work and Thermodynamics
The Kinetic Theory picture of a gas (outlined in the previous lecture) is often called the
Ideal Gas Model
.
It ignores interactions between molecules, and the finite size of
molecules. In fact, though, these only become important when the gas is very close to the
temperature at which it become liquid, or under extremely high pressure.
In this lecture,
we will be analyzing the behavior of gases in the pressure and temperature range
corresponding to heat engines, and in this range the Ideal Gas Model is an excellent
approximation.
Essentially, our program here is to learn how gases absorb heat and turn
it into work, and
vice versa
. This heat-work interplay is called
thermodynamics
.
Julius Robert Mayer was the first to appreciate that there
is
an equivalence between heat
and mechanical work. The tortuous path that led him to this conclusion is described in an
earlier lecture, but once he was there, he realized that in fact the numerical equivalence—
how many Joules in one calorie in present day terminology—could be figured out easily
from the results of some measurements of gas specific heat by French scientists.
The key
was that they had measured specific heats both at constant
volume
and at constant
pressure
.
Mayer realized that in the latter case, heating the gas necessarily increased its
volume, and the gas therefore did work in pushing to expand its container.
Having
convinced himself that mechanical work and heat were equivalent, evidently the extra
heat needed to raise the temperature of the gas at constant pressure was exactly the work
the gas did on its container.
(
Historical note
: although he did the work in 1842, he didn’t
publish until 1845, and at first miscalculated—but then gave a figure within 1% of the
correct value of 4.2 joules per calorie.)
The simplest way to see what’s going on is to imagine the gas in a cylinder, held in by a
piston, carrying a fixed weight, able to move up and down the cylinder smoothly with
negligible friction. The pressure on the gas is just the total weight pressing down divided
by the area of the piston, and this total weight, of course, will not change as the piston
moves slowly up or down: the gas is at
constant pressure
.