Physical Chemistry Third Edition

40 2 Work, Heat, and Energy: The First Law of Thermodynamics

2.1 Work and the State of a System

Thermodynamics involves work and heat. It began in the 19th century with the

efforts of engineers to increase the efficiency of steam engines, but it has become

the general theory of the macroscopic behavior of matter at equilibrium. It is

based on empirical laws, as is classical mechanics. Although classical mechanics

has been superseded by relativistic mechanics and quantum mechanics, thermody-

namics is an unchallenged theory. No exceptions have been found to the laws of

thermodynamics.

Mechanical Work

The quantitative measurement of work was introduced by Carnot, who defined an

amount of work done on an object as the height it is lifted times its weight. This

definition was extended by Coriolis, who provided the presently used definition of

work:The amount of work done on an object equals the force exerted on it times the

distance it is moved in the direction of the force.If a forceFzis exerted on an object in

thezdirection, the work done on the object in an infinitesimal displacementdzin the

zdirection is

dwFzdz (definition of work) (2.1-1)

wheredwis the quantity of work. The SI unit of force is the newton (Nkgms−^2 ),

and the SI unit of work is the joule (Jkg m^2 s−^2 N m),

Nicolas Leonard Sadi Carnot, 1796–1832,

was a French engineer who was the

first to consider quantitatively the

interconversion of work and heat and

who is credited with founding the

science of thermodynamics.

Gaspard de Coriolis, 1792–1843, was a
French physicist best known for the
Coriolis force.

If the force and the displacement are not in the same direction, they must be

treated as vectors. A vector is a quantity that has both magnitude and direction. Vectors

are discussed briefly in Appendix B. We denote vectors by boldface letters and denote

the magnitude of a vector by the symbol for the vector between vertical bars or by

the letter in plain type. The amount of workdwcan be written as thescalar product

of the two vectorsFanddrwhereFis the force exerted on the object anddris its

displacement:

dwF·dr|F||dr|cos(α) (2.1-2)

whereαdenotes the angle between the vectorFand the vectordr. The scalar pro-

duct of the vectorsFanddr, denoted byF·dr, is defined by the second equality in

Eq. (2.1-2), which contains the magnitudes of the vectors. The product|dr|cos(α)is

the component of the displacement in the direction of the force, as shown in Figure 2.1.

Only the component of the displacement in the direction of the force is effective in

determining the amount of work. There is no work done if the object does not move

or if the force and the displacement are perpendicular to each other. For example, if

the earth’s orbit around the sun were exactly circular, the sun would do no work on the

earth.

dr cos(

a)

a

dr

F

Figure2.1AForceanda
Displacement.

The formula in Eq. (2.1-2) can be written in terms of Cartesian components as in

Eq. (B-35) of Appendix B:

dwFxdx+Fydy+Fzdz (2.1-3)