Page 68 - Physical Chemistry

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internal energy of 20 g of H O at a given T and P is twice the internal energy of 10 g Section 2.4
2
of H O at that T and P. For a pure substance, the molar internal energy U is The First Law of Thermodynamics
m
2
defined as
U U>n (2.36)
m
where n is the number of moles of the pure substance. U is an intensive property that
m
depends on P and T.
We usually deal with closed systems. Here, the system’s mass is held fixed.
Besides changing the mass of a system by adding or removing matter, we can
change the energy of a system by doing work on it or by heating it. The first law of
thermodynamics asserts that there exists an extensive state function E (called the
total energy of the system) such that for any process in a closed system

¢E q w closed syst. (2.37)
where E is the energy change undergone by the system in the process, q is the heat
flow into the system during the process, and w is the work done on the system during
the process. The first law also asserts that a change in energy E of the system is
accompanied by a change in energy of the surroundings equal to E, so the total
energy of system plus surroundings remains constant (is conserved). For any process,
E syst E surr 0 (2.38)
We shall restrict ourselves to systems at rest in the absence of external fields. Here
K 0 V, and from (2.35) we have E U. Equation (2.37) becomes
¢U q w closed syst. at rest, no fields (2.39)*
where U is the change in internal energy of the system. U is an extensive state
function.
Note that, when we write U, we mean U syst . We always focus attention on the
system, and all thermodynamic state functions refer to the system unless otherwise
specified. The conventions for the signs of q and w are set from the system’s viewpoint.
When heat flows into the system from the surroundings during a process, q is positive
(q 0); an outflow of heat from the system to the surroundings means q is negative.
When work is done on the system by the surroundings (for example, in a compression
of the system), w is positive; when the system does work on its surroundings, w is neg-
ative. A positive q and a positive w each increase the internal energy of the system.
For an infinitesimal process, Eq. (2.39) becomes

dU dq dw closed syst. (2.40)
where the other two conditions of (2.39) are implicitly understood. dU is the infini-
tesimal change in system energy in a process with infinitesimal heat dq flowing into
the system and infinitesimal work dw done on the system.
The internal energy U is (just like P or V or T) a function of the state of the
system. For any process, U thus depends only on the final and initial states of the
system and is independent of the path used to bring the system from the initial state to
the final state. If the system goes from state 1 to state 2 by any process, then
¢U U U U final U initial (2.41)*
2
1
The symbol always means the final value minus the initial value.
A process in which the final state of the system is the same as the initial state is
called a cyclic process; here U U , and
2
1
¢U 0 cyclic proc. (2.42)
which must obviously be true for the change in any state function in a cyclic process.