Concise Physical Chemistry

c03 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come

STATE FUNCTIONS 41

3.3.2 Back to Line Integrals

Suppose some propertyf(x,y) is associated with a curveCin thex–yplane and we

wish to find the line integral between certain limits along that curve. The appropriate

integral is

I=

∫

C

f(x,y)ds

The integration is to be carried out, not along an axis as in the case of a simple

integral, but along the curve inx–yspace. If we havey=f(x) that specifies the path

in thex–yplane, we also havedsalong the curve from Section 3.3.1 so the integral is

I=

∫

C

f(x,y)

(

1 +

(

dy

dx

) 2 )^1 /^2

dx=

∫

C

f(x,f(x))

(

1 +

(

dy

dx

) 2 )^1 /^2

dx

3.4 THERMODYNAMIC STATES AND SYSTEMS

A thermodynamicsystemis any part of theuniversewe want to look at. The rest of

the universe is itssurroundings.

system+surroundings=universe

A system is usually defined in such a way as to be manageable; for example, a

reaction flask containing chemicals is a system. The surroundings may be a constant

temperature bath in which the system is immersed, along with the rest of the universe.

Anisolated systemdoes not exchange energy or matter with its surroundings. Aclosed

systemexchanges energy, but not matter, with the surroundings. A piston fitted to

a cylinder that can do work and exchange heat with its surroundings, but does not

leak, is a closed system. Anopen systemexchanges both energy and matter with its

surroundings. An animal or plant is an open system.

3.5 STATE FUNCTIONS

Athermodynamic state functionis one of severalconservedmathematical functions

describing a property of a system. Energy is a thermodynamic state function. The

termthermodynamic propertyis used in the same way. To define thestateof a system,

we must describe it inallof its physical properties, but we already know that there

are only three degrees of freedom for a pure substance, two if you specifymolar

properties as we normally do. In nonuniform systems, one of the variables may be

different at different locations. For example, the temperature may not be the same

everywhere in a closed room. Other variables will then be nonuniform as well. These

systems are more difficult to treat mathematically, but they have been described in a