Concise Physical Chemistry

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

44 THE THERMODYNAMICS OF SIMPLE SYSTEMS

for an ideal gas. We can also define anadiabaticprocess, which is a perfectly insulated

process. Before doing so, we shall need the concept of heat capacity.

3.7 HEAT CAPACITY

When heatqis put into a system its temperature rises. The change in temperature is

proportional to the amount of heat

q=CT

whereCis a proportionality constant.Cdepends on both the nature of, say, a chemical

substance and the amount taken; it is an extensive property (Section 1.6).Cis really

a parameter because it is different for different substances. It is common experience

that metals heat up faster over a flame than does water. They have differentcapacities

to absorbheat; hence the parameterCis called theheat capacity.

To use calculus in working with the heat capacity, it is necessary to replace the ap-

proximate macroscopic observationC=q/Twith the infinitesimalC=dq/dT.

Furthermore, we chemists carry our ordinary bench reactions under conditions of

constant (atmospheric) pressure, and thermochemists carry out combustion reactions

inside a closed bomb. The heat capacity under constant volume conditions is not

exactly the same as the heat capacity under constant pressure conditions, so we

distinguish between the two heat capacitiesCVandCpas

CV=

(

∂q

∂T

)

V

and Cp=

(

∂q

∂T

)

p

The infinitesimals in the heat capacity equations are partials because each parameter

is defined holding eitherVorpconstant.

3.8 ENERGY AND ENTHALPY

Having stipulated constant volume for the first of the heat capacity expressions, the

workpdVdisappears for a system that can do only work of expansiondVagainst a

pressurep

dU=dq+pdV

Consequently,

CV≡

(

∂q

∂T

)

V

=

(

∂U

∂T

)

V