1549380323-Statistical Mechanics Theory and Molecular Simulation

56 Theoretical foundations

2.2 The laws of thermodynamics

Our discussion of the laws of thermodynamics will make no referenceto the microscopic
constituents of a particular system. Concepts and definitions we will need for the
discussion are described below:

i. Athermodynamicsystem is a macroscopic system. Thermodynamics always di-

vides the universe into the system and its surroundings. A thermodynamic system

is said to beisolatedif no heat or material is exchanged between the system and

its surroundings and if the surroundings produce no other changein the thermo-

dynamic state of the system.

ii. A system is inthermodynamic equilibriumif its thermodynamic state does not

change in time.

iii. The fundamental thermodynamic parameters that define a thermodynamic state,

such as the pressureP, volumeV, the temperatureT, and the total massMor

number of molesnare measurable quantities assumed to be provided experimen-

tally. A thermodynamicstateis specified by providing values of all thermodynamic

parameters necessary for a complete description of a system.

iv. Theequation of stateof a system is a relationship among the thermodynamic

parameters prescribing how these parameters vary from one equilibrium state to

another. Thus, ifP,V,T, andnare the fundamental thermodynamic parameters

of a system, the equation of state takes the general form

g(n,P,V,T) = 0. (2.2.1)

As a consequence of eqn. (2.2.1), there are in fact only three independent thermo-

dynamic parameters in an equilibrium state. When the number of molesremains

fixed, the number of independent parameters is reduced to two. An example of

an equation of state is that of anideal gas, which is defined (thermodynamically)

as a system whose equation of state is

PV−nRT= 0, (2.2.2)

whereR= 8.315 J·mol−^1 ·K−^1 is thegas constant. The ideal gas represents the

limiting behavior of all real gases at sufficiently low densityρ≡n/V.

v. Athermodynamic transformationis a change in the thermodynamic state of a

system. In equilibrium, a thermodynamic transformation is effectedby a change

in the external conditions of the system. Thermodynamic transformations can be

carried out eitherreversiblyorirreversibly. In a reversible transformation, the

change is carried out slowly enough that the system has time to adjust to each

new external condition imposed along a prescribed thermodynamic path, so that

the system can retrace its history along the same path between the endpoints of

the transformation. If this is not possible, then the transformation is irreversible.

vi. Astate functionis any functionf(n,P,V,T) whose change under any thermody-

namic transformation depends only on the initial and final states ofthe transfor-

mation andnoton the particular thermodynamic path taken between these states

(see Fig. 2.1).