5.1.3 Heat
“Heat,” notatedQ, is used in thermodynamics as a term for
an amount of thermal energy that is transferred. When you put a
bite of food in your mouth that is too hot, the pain is caused by the
heat transferred from the food to your mouth. People discussing the
weather may say “What about this heat today?” or “What about
this temperature today?” as if the words were synonyms, but to a
physicist they are distinct. Temperature is not additive, but heat
is: two sips of hot coffee have the same temperature as one, but
two sips will transfer twice the heat to your mouth. Temperature is
measured in degrees, heat in joules.
If I give you an object, you can measure its temperature —
physicists call temperature a “property of state,” i.e., you can tell
what it is from the current state of the object. Heat is a description
of aprocessof energy transfer, not a property of state.
It’s relatively easy to detect and measure atransferof thermal
energy (the hot bite of food), but to say how much thermal energy an
objecthasis much harder — sometimes even impossible in principle.
Heat is distinguished from mechanical work (3.2.8, p. 164) be-
cause work is the transfer of energy by a macroscopically measurable
force, e.g., the force of a baseball bat on the ball. No such force is
needed in order to melt an ice cube; the forces are in microscopic
collisions of water molecules with ice molecules.
Heat, like the flow of money or water, is a signed quantity, but
the sign is a matter of definition. The bank’s debit is the customer’s
withdrawal. It is an arbitrary choice whether to callQpositive when
it flows from object A to object B or from B to A, and likewise
for the workW. Similar choices arise in the description of flowing
fluids (example 1, p. 58) or electric currents (sec. 9.1.1, p. 530). We
will usually adopt definitions such that as many heats and works as
possible are positive. So by our definition, a cute 19th-century steam
locomotive takes in positive heat from its boiler, does positive work
to pull the cars, and spews out positive heat through its smokestack.
When only a single object is being discussed, such as a cylinder
of compressed air, we define a heat input as positive and a work
output as positive, which is again in accord with the picture of the
cute steam engine. No universally consistent convention is possible,
since, e.g., if objects A, B, and C all interact, we will always have
opposite signs for A’s work on B and B’s work on A, etc.
Discussion Questions
A Figure j/1 shows objects 1 and 2, each with a certain temperatureT
and a certain amount of thermal energyE. They are connected by a thin
rod, so that eventually they will reach thermal equilibrium. We expect that
the rate at which heat is transferred into object 1 will be given by some
equation dE 1 /dt=k(...), wherekis a positive constant of proportionality
and “...” is some expression that depends on the temperatures. Suppose
Section 5.1 Pressure, temperature, and heat 315