



[TOP]
1. The internal energy


[TOP]
Open, closed and isolated systems:


[TOP]
Heat and work  the sign conventions: [ TOP ]
Heat, Q
Fig. 1: Heat energy transfer [ TOP ]
Work, w
[ TOP ]
PV work
Since P_{ext} = Force / crosssectional area, then: Note: 

[TOP]
Internal energy and internal energy
changes, U and DU
The internal energy of a system, U, is the total energy of the system, i.e. the sum of the potential energy (PE) and kinetic energy (KE).
(ii) The KE is due to motion  vibrations in solids rotations and translations in fluids. The KE is 0 at 0K. Note: (1) Estimates of the internal energy may be obtained from statistical thermodynamics (e.g. in molecualr modelling). (2) Rather than the absolute values of the internal energy (U), we usually speak of changes in the internal energy, DU. (3) See also the first law of thermodynamics.


[TOP]
State Functions: A state function refers to a property whose 'value' depends solely on the state of the system, and NOT dependent on the way that this state is achieved. In particular, the work done, w, and heat energy transferred, q, are NOT state functions (see fig. 1), whilst the internal energy U is. The most commonly used feature of a state function, (U, for example),
is that we may write:
............................................................... (eqn. 1)
Another important property of state functions, is that a function which
is solely composed from other state functions is itself a state function.
composed up from sum of two or more state functions. For example, since
U,
P and V are state functions, the enthalpy H defined
as below is also a state function.
...............................................................(eqn. 2) We shall now present the properties of state function in the rigour
of the mathematical notation:
(1) Integration of a state function U must have a definite
value which is independent of the path of integration (in between
the limits A and B).
...............................................................(eqn. 3)
(2) Since U is an exact differential, if U is determined by the
values of the variables x and y, then:
................................ (eqn. 4)
(3) The order of differentiation of a state function is immaterial,
i.e.:
.................................. (eqn. 5) 

[TOP]
The first law of thermodynamics The first law of thermodynamics states:(1) The Dw term in first law may be expressed in terms of the PV work, i.e.: DU = DQ  p_{ex}DV(2) If the volume is fixed, then: DU = DQ + 0 = DQ _{V}
DU = 0 = DQ + Dw => DQ = DwThis is beacuse:(1) at isothermal conditions, the KE contribution remains constantIt means that: 