University Physics I - Classical Mechanics, 2019

304 CHAPTER 13. THERMODYNAMICS
(waves) in which the constituent parts of an object move relative to each other in a way that
looks “organized,” or synchronized, from a macroscopic perspective. What is needed next is
to account for the random motion, on a microscopic scale, of the smallest parts (atoms or
molecules) that make up an extended object. This motion is constantly happening, and it is
a key ingredient of the concepts of thermal energy and temperature.
Conceptually, thermodynamics involves the introduction of two new physical quantities, temperature
and entropy. Temperature will be introduced in this lecture, and entropy in the next one. It
is interesting to note from the start, however, that these are very different from all the quantities
we have introduced so far this semester, in a fundamental way. In classical physics, at least, there
is no difficulty in extending all those other quantities to the study of the smallest parts making
up an object: we can perfectly well talk about the position, velocity or energy of a molecule. But
temperature and entropy are statistical quantities, which are only properly defined, from a fundamental
point of view, for a large collection of (small) subsystems: it makes no sense to speak about
the temperature or the entropy of a single molecule. This shows that there was really a profound
change in perspective and methodology in classical physics when statistical mechanics (the part of
physics that provides a microscopic foundation for thermodynamics) was developed.
13.2 Introducing temperature
13.2.1 Temperature and heat capacity
The change in perspective that I just mentioned also means that it is not easy to even define
temperature, beyond our natural intuition of “hot” and “cold,” or the somewhat circular notion
that temperature is simply “what thermometers measure.” Roughly speaking, though, temperature
is a measure of the amount (or, to be somewhat more precise, the concentration) of thermal energy
in an object. When we directly put an amount of thermal energy, ΔE th (what we will be calling
heat in a moment), in an object, we typically observe its temperature to increase in a way that is
approximately proportional to ΔE th , at least as long as ΔE th is not too large:
ΔT = ΔE th
C
(13.1)
The proportionality constant C is called the heat capacity of the object: according to Eq. (13.1), a
system with a large heat capacity could absorb (or give off—the equation is supposed to apply in
either case) a large amount of thermal energy without experiencing a large change in temperature.
If the system does not do any work in the process (recall Eq. (7.20)!), then its internal energy will
increase (or decrease) by exactly the same amount of thermal energy it has taken in (or given off) 1 ,
1 If the system does do some work (or has work done on it), then Eq. (13.8) applies; see below.