termodinamics

HEAT AND INTERNAL ENERGY
At the outset, it is important that we make a major distinction between internal energy
and heat. Internal energy is all the energy of a system that is associated
with its microscopic components—atoms and molecules—when viewed
from a reference frame at rest with respect to the object. The last part of this
sentence ensures that any bulk kinetic energy of the system due to its motion
through space is not included in internal energy. Internal energy includes kinetic
energy of translation, rotation, and vibration of molecules, potential energy within
molecules, and potential energy between molecules. It is useful to relate internal
energy to the temperature of an object, but this relationship is limited—we shall
find in Section 20.3 that internal energy changes can also occur in the absence of
temperature changes.
As we shall see in Chapter 21, the internal energy of a monatomic ideal gas is
associated with the translational motion of its atoms. This is the only type of energy
available for the microscopic components of this system. In this special case,
the internal energy is simply the total kinetic energy of the atoms of the gas; the
higher the temperature of the gas, the greater the average kinetic energy of the
atoms and the greater the internal energy of the gas. More generally, in solids, liquids,
and molecular gases, internal energy includes other forms of molecular energy.
For example, a diatomic molecule can have rotational kinetic energy, as well
as vibrational kinetic and potential energy.
Heat is defined as the transfer of energy across the boundary of a system
due to a temperature difference between the system and its surroundings.
When you heat a substance, you are transferring energy into it by placing it in
contact with surroundings that have a higher temperature. This is the case, for example,
when you place a pan of cold water on a stove burner—the burner is at a
higher temperature than the water, and so the water gains energy. We shall also
use the term heat to represent the amount of energy transferred by this method.
Scientists used to think of heat as a fluid called caloric, which they believed was
transferred between objects; thus, they defined heat in terms of the temperature
changes produced in an object during heating. Today we recognize the distinct
difference between internal energy and heat. Nevertheless, we refer to quantities
20.1
U
Heat
James Prescott Joule British
physicist (1818–1889) Joule received
some formal education in
mathematics, philosophy, and chemistry
but was in large part selfeducated.
His research led to the
establishment of the principle of
conservation of energy. His study of
the quantitative relationship among
electrical, mechanical, and chemical
effects of heat culminated in his discovery
in 1843 of the amount of work
required to produce a unit of energy,
called the mechanical equivalent of
heat. (By kind permission of the President
and Council of the Royal Society)
10.3
604 CHAPTER 20 Heat and the First Law of Thermodynamics
using names that do not quite correctly define the quantities but which have become
entrenched in physics tradition based on these early ideas. Examples of such
quantities are latent heat and heat capacity.
As an analogy to the distinction between heat and internal energy, consider
the distinction between work and mechanical energy discussed in Chapter 7.
The work done on a system is a measure of the amount of energy transferred to
the system from its surroundings, whereas the mechanical energy of the system
(kinetic or potential, or both) is a consequence of the motion and relative positions
of the members of the system. Thus, when a person does work on a system,
energy is transferred from the person to the system. It makes no sense to talk
about the work of a system—one can refer only to the work done on or by a system
when some process has occurred in which energy has been transferred to or
from the system. Likewise, it makes no sense to talk about the heat of a system—
one can refer to heat only when energy has been transferred as a result of a temperature
difference. Both heat and work are ways of changing the energy of a
system.
It is also important to recognize that the internal energy of a system can be
changed even when no energy is transferred by heat. For example, when a gas is
compressed by a piston, the gas is warmed and its internal energy increases, but no
transfer of energy by heat from the surroundings to the gas has occurred. If the
gas then expands rapidly, it cools and its internal energy decreases, but no transfer
of energy by heat from it to the surroundings has taken place. The temperature
changes in the gas are due not to a difference in temperature between the gas and
its surroundings but rather to the compression and the expansion. In each case,
energy is transferred to or from the gas by work, and the energy change within the
system is an increase or decrease of internal energy. The changes in internal energy
in these examples are evidenced by corresponding changes in the temperature
of the gas.
Units of Heat
As we have mentioned, early studies of heat focused on the resultant increase in
temperature of a substance, which was often water. The early notions of heat based
on caloric suggested that the flow of this fluid from one body to another caused
changes in temperature. From the name of this mythical fluid, we have an energy
unit related to thermal processes, the calorie (cal), which is defined as the
amount of energy transfer necessary to raise the temperature of 1 g of water
from 14.5°C to 15.5°C.1 (Note that the “Calorie,” written with a capital “C”
and used in describing the energy content of foods, is actually a kilocalorie.) The
unit of energy in the British system is the British thermal unit (Btu), which is defined
as the amount of energy transfer required to raise the temperature of
1 lb of water from 63°F to 64°F.
Scientists are increasingly using the SI unit of energy, the joule, when describing
thermal processes. In this textbook, heat and internal energy are usually measured
in joules. (Note that both heat and work are measured in energy units. Do
not confuse these two means of energy transfer with energy itself, which is also measured
in joules.)
The calorie
1 Originally, the calorie was defined as the “heat” necessary to raise the temperature of 1 g of water by
1°C. However, careful measurements showed that the amount of energy required to produce a 1°C
change depends somewhat on the initial temperature; hence, a more precise definition evolved.
20.1 Heat and Internal Energy 605
The Mechanical Equivalent of Heat
In Chapters 7 and 8, we found that whenever friction is present in a mechanical
system, some mechanical energy is lost—in other words, mechanical energy is not
conserved in the presence of nonconservative forces. Various experiments show
that this lost mechanical energy does not simply disappear but is transformed into
internal energy. We can perform such an experiment at home by simply hammering
a nail into a scrap piece of wood. What happens to all the kinetic energy of the
hammer once we have finished? Some of it is now in the nail as internal energy, as
demonstrated by the fact that the nail is measurably warmer. Although this connection
between mechanical and internal energy was first suggested by Benjamin
Thompson, it was Joule who established the equivalence of these two forms of
energy.
A schematic diagram of Joule’s most famous experiment is shown in Figure
20.1. The system of interest is the water in a thermally insulated container. Work is
done on the water by a rotating paddle wheel, which is driven by heavy blocks
falling at a constant speed. The stirred water is warmed due to the friction between
it and the paddles. If the energy lost in the bearings and through the walls is neglected,
then the loss in potential energy associated with the blocks equals the work
done by the paddle wheel on the water. If the two blocks fall through a distance h,
the loss in potential energy is 2mgh, where m is the mass of one block; it is this energy
that causes the temperature of the water to increase. By varying the conditions
of the experiment, Joule found that the loss in mechanical energy 2mgh is proportional
to the increase in water temperature T. The proportionality constant was
found to be approximately 4.18 J/g °C. Hence, 4.18 J of mechanical energy raises
the temperature of 1 g of water by 1°C. More precise measurements taken later
demonstrated the proportionality to be 4.186 J/g °C when the temperature of the