Page 93 - Essentials of physical chemistry

The First Law of Thermodynamics 55

through metal walls of a cylinder, so we can model the events within the cylinder as a system
thermally isolated from the outside world for a short time interval. Then we can enlarge the domain
of the system and consider the energy and heat flow in a region around the engine to consider
the whole engine as a unit but isolated from the environment. Lastly, we might want to consider the
effect of various thermal devices on the whole planet Earth as an isolated system in space. Thus,
the concept of the ‘‘system’’ is largely a matter of choosing a region and a time interval on the part of
the person doing the analysis.

q > 0, heat energy is absorbed (by the system)
q < 0, heat energy is given off (to the environment)
w > 0, work done on the system by the environment, especially on a gas
w < 0, work done by the system on the environment; especially by a gas

U, internal energy of the system, contains molecular translational, rotational, and vibrational
energy relative to a preexisting energy scale of elemental formation in chemistry. Chemistry is
‘‘post-creation,’’ the elements are already here with their characteristic electronic energy levels and
chemistry studies interactions between elements. Chemical thermodynamics functions at a level of
ground state electronic energy levels of the elements. Nuclear chemistry involves a scale of internal
energy units relegated to physics.

D (after – before), this is an order-specific convention definition in all of thermodynamics
DT ¼ 0 means ‘‘isothermal,’’ same temperature, constant temperature
Dq ¼ 0 means ‘‘adiabatic,’’ constant heat, no heat flow
DP ¼ 0 means ‘‘isobaric,’’ constant pressure, no change in pressure

Laboratory variables: P, V, T, n, SI units are bars, L, 8K, mol but other units do exist.

FIRST LAW OF THERMODYNAMICS

With the definitions and sign conventions above, we can state a simple form of the first law.
dU ¼ d =q þ d=w

In words, this means that the change in internal energy occurs as a change in heat and a change in
work. The question in applications is how much change there is in heat and work for a given change
in internal energy. Much of the credit for the first law is due to James P. Joule (1818–1889) [3] who
was an English physicist who carried out a number of important experiments relating heat and work.
An interested student should look up short biographies of Joule on the Internet to appreciate the
controversy surrounding his experiments. His several measurements of the relationship between
heat in calories and mechanical work (1 cal ¼ 4.184 J) eventually triumphed over the ‘‘caloric’’
theory. A warning is needed here regarding the sign of the work term. Many older texts formulate
the work term as dw because almost all the applications involve gases, which expand to push some
sort of a piston to do work. In the last 20 years or so almost all texts give the first law with þdw but
it all works out fine since compressing a gas is positive work while expanding gas is negative work
on the gas but positive work on the environment. This first example shows us that we need to think
about the way in which the system and environment act during a given process and worry over using
the correct sign of the variables.
Now it is the time to remind ourselves that energy is conserved and that U represents some
amount of energy involved in a given process. As such we can represent the change in energy as:
DU ¼ U after U before :