Internal Energy Eint , Heat Q, and Specific
Heat c
From mechanics we found energy comes to us in various
forms: kinetic energy associated with translational and
rotational motion and potential energies associated with
various conservative forces.
In thermodynamics another form of energy is introduced.
Therefore, consider the prototypical thermodynamic system
(a gas in a cylinder with a piston). If the system translates
or rotates then we say the system as a whole has kinetic
energy. But if we pin the system down and don’t allow it to
translate or rotate as a whole, there is still kinetic energy
present due to the random motion of the atoms of the
system. In addition, these atoms might exert forces on each
other and therefore, there could be internal potential
energies associated with these “bonds”. But in the simplest
system, a monatomic ideal gas (mig), there are no bonds
and have only random kinetic energy.
The internal energy of a system is defined as the total of
the random internal kinetic energies of the atoms plus the
total internal potential energies due to the bonds between
atoms if such bonds exist.
Thus, internal energy is not a new concept or form of
energy. On the other hand, heat is a new and is also central
to thermodynamics. Heat is defined as an energy
TRANSFER process. Heat is an energy transfer between
two objects of different temperatures due only to their
temperature difference. Ultimately the transfer is due to the
collisions between the atoms—thus, the connection of heat
with mechanics.
This notion of heat is called the mechanical model of heat
and it became the dominant view in the mid-1800’s
following the famous Joule mechanical equivalent of heat
experiment. Before Joule people believed heat to be an
invisible, weightless fluid that flowed between two objects
that have a different temperature. The fluid was called
caloric, therefore, this was called the caloric model of heat.
A useful analogy is a pond and rain. A pond contains so
much water (like internal energy) but this can increase due
to rain (like heat or work).
The thermal properties of an object or material are an
important way of characterizing the system. One of the
most important thermal properties is found when an amount
of energy, Q, is delivered to the object by heating. Often Q
causes the temperature of the object to change by T. If for
a given T, Q has to be large, we say the object can “hold a
lot of heat” and therefore, it has a large heat capacity, C,
defined by,
C  Q/T.
C is a property of an object, it will depend on the
composition of the object but also the mass of the object.
Consequently, for the same material, C will be bigger if
there is a lot of mass of the material present compared to
having a small amount of the material.
A related term called specific heat, c, depends only on the
material of the object and not on the mass of the object,
c  C/m = Q/mT.
Measured values of c are tabulated in your textbook.
Values of C are not given in tables since C depends on the
amount of mass present.
Rearranging we have,
Q = mcT.
APPLICATION: Calorimetry
In calorimetry we mix together two substances that start
with different temperatures and wait until thermal
equilibrium is achieved at a final temperature, Tf.
Measuring the mass of each constitutent and all of these
temperatures allows one to find the specific heat of one of
the constituents provided you know the specific heat of the
other constituent.
The fundamental principle used is energy conservation,
which takes the guise
|Qgained by one constituent| = |Qloss by the other constituent|
EXAMPLES [in class]