1549380323-Statistical Mechanics Theory and Molecular Simulation

Laws of thermodynamics 57

P

V

T

2

1

Fig. 2.1The thermodynamic state space defined by the variablesP,V, andTwith two paths

(solid and dashed lines) between the state points 1 and 2. Thechange in a state function

f(n,P,V,T) is independent of the path taken between any two such state points.

vii. In order to change the volume or the number of moles, work mustbe performed

on a system. If a transformation is performed reversibly such that the volume

changes by an amount dV and the number of moles changes by an amount dn,

then the work performed on the system is

dWrev=−PdV+μdn. (2.2.3)

The quantityμis called thechemical potential, defined to be the amount of
work needed to add 1.0 mole of a substance to a system already containing that
substance.
viii. In order to change the temperature of a system, heat must beadded or removed.
The amount of heat dQneeded to change the temperature by an amount dTin
a reversible process is given by

dQrev=CdT. (2.2.4)

The quantityCis called theheat capacity, defined to be the amount of heat

needed to change the temperature of 1.0 mole of a substance by 1.0degree on a

chosen scale. If heat is added at fixed pressure, then the heat capacity is denoted

CP. If heat is added at fixed volume, it is denotedCV.

2.2.1 The first law of thermodynamics

The first law of thermodynamics is a statement of conservation of energy. We saw in

Section 1.6 that performing work on a system changes its potential(or internal) energy

(see Section 1.4). Thermodynamics recognizes that heat is also a form of energy. The