Page 30 - Bruno Linder Elementary Physical Chemistry

August 25, 2010 9:36 9in x 6in b985-ch02 Elementary Physical Chemistry

The First Law of Thermodynamics 15

(The minus sign is introduced, because one of the dT ’s has to be negative
and we require the C’s to be positive.) If a particular value is assigned to
one of the heat capacities, the other is automatically established.
Once heat capacity is defined, heat transferred can be expressed by the
relation,
q/∆T = C (2.6a)

or dq = CdT (2.6b)

For macroscopic systems,
q = ∫ CdT (2.7)
and, if the heat capacity is constant, q = C∆T .

2.7. Internal Energy
When the surrounding does work on or supplies heat to the system, the
surrounding loses energy. But energy cannot be lost or gained — energy
must be conserved. The energy lost by the surrounding is gained by the
system in the form of internal energy. [Note: since the advent of relativity,
energy and matter can be interconverted, and a more accurate statement
would be: Energy–matter must be conserved.]
Conservation of energy in Thermodynamics is effectively the First Law
of Thermodynamics. It can be expressed as

∆U = q + w (2.8)
where, in general, w stands for total work: w = w PV + w other .
Convention about signs
In this course, as indicated previously, (and used in most scientific but not
engineering treatments,) w represents the work done by the surrounding on
the system and q is the heat supplied by the surrounding to the system.

Comment: Consistent with this convention is the formula dw PV =
−P ext dV , which tells us that w is positive in a compression and
negative in an expansion. [Engineers often use the convention that
work is positive when done by the system on the surrounding, and
their First Law reads ∆U = q − w.]