Physical Chemistry Third Edition

42 2 Work, Heat, and Energy: The First Law of Thermodynamics

wherePis the pressure of the gas andAis the area of the piston. We define theexternal

pressurePextby

Pext

Fext

A

(definition ofPext) (2.1-7)

At equilibrium there is no tendency for the piston to move so that

PPextP(transmitted) (at equilibrium) (2.1-8)

where we define thetransmitted pressureby

P(transmitted)

F(transmitted)

A

(2.1-9)

Areversible processis defined to be one that can be reversed in direction by an

infinitesimal change in the surroundings. In order for an infinitesimal change inPext

to change the direction of motion of the piston, there can be no friction and there

can be no more than an infinitesimal difference betweenP,P(transmitted), andPext.

For an infinitesimal step of a reversible process the work done on the surroundings is

given by

dwsurr,revPdV (reversible process) (2.1-10)

whereVis the volume of the system. We will consistently use a subscript “surr” when a

symbol pertains to the surroundings. If no subscript is attached to a symbol, the symbol

refers to the system.

If a fluid system contains a single substance in a single phase, its equilibrium state

can be specified by the values of three variables such asT,V, andn. We can define

a three-dimensional space in whichT,V, andnare plotted on the three axes. We call

such mathematical space astate space. Each equilibrium state is represented by astate

pointlocated in the state space. A reversible process proceeds infinitely slowly, so that

the system has sufficient time to come to equilibrium during any part of the process.

The system passes through a succession of equilibrium states and the state point traces

out a curve in the equilibrium state space, such as that shown in Figure 2.3 for a fixed

value ofn.

We reckon work done on the surroundings as a negative amount of work done on

the system, so we write

dwrev−PdV (2.1-11)

The signs we have used correspond to the following convention:A positive value ofw

ordwcorresponds to work being done on the system by the surroundings. A negative

value ofwor ofdwcorresponds to work being done on the surroundings by the system.

Unfortunately, the opposite convention has been used in some older books. We will

consistently use the convention stated above.

We have obtained the relation of Eq. (2.1-11) for a gas in a cylinder with a movable

piston. We assert that this relation applies to a fluid system of any shape. If a system

can exchange work with its surroundings only by changing its volume, we say that it

is asimple system. This kind of work is sometimes calledcompression workorP-V

work. A gas is a simple system. A liquid is a simple system if the work required to

create surface area by changing the shape of the system can be neglected. A spring or

a rubber band is not a simple system because work is done to change its length. An

electrochemical cell is also not a simple system since work can be done by passing a

current through it.