Page 68 - Physical chemistry eng

3 CHAPTER

The Importance of 3.1 The Mathematical Properties
of State Functions
State Functions: 3.2 The Dependence of U on V
and T
3.3 Does the Internal Energy
Internal Energy Depend More Strongly on V
or T?
3.4 The Variation of Enthalpy
and Enthalpy with Temperature at
Constant Pressure
3.5 How Are C P and C V Related?
3.6 The Variation of Enthalpy
with Pressure at Constant
Temperature
The mathematical properties of state functions are utilized to express
3.7 The Joule-Thomson
the infinitesimal quantities dU and dH as exact differentials. By doing so, Experiment
expressions can be derived that relate the change of U with T and V and the 3.8 Liquefying Gases Using an

change in H with T and P to experimentally accessible quantities such as the Isenthalpic Expansion
heat capacity and the coefficient of thermal expansion. Although both U
and H are functions of any two of the variables P, V, and T, the dependence
of U and H on temperature is generally far greater than the dependence on
P or V. As a result, for most processes involving gases, liquids, and solids, U
and H can be regarded as functions of T only. An exception to this state-
ment is the cooling on the isenthalpic expansion of real gases, which is com-

mercially used in the liquefaction of N 2 , O 2 , He, and Ar.

The Mathematical Properties of State
3.1 Functions

In Chapter 2 we demonstrated that U and H are state functions and that w and q are path
functions. We also discussed how to calculate changes in these quantities for an ideal
gas. In this chapter, the path independence of state functions is exploited to derive rela-
tionships with which ¢U and ¢H can be calculated as functions of P, V, and T for real
gases, liquids, and solids. In doing so, we develop the formal aspects of thermodynam-
ics. We will show that the formal structure of thermodynamics provides a powerful aid
in linking theory and experiment. However, before these topics are discussed, the math-
ematical properties of state functions need to be outlined.
The thermodynamic state functions of interest here are defined by two variables from
the set P, V, and T. In formulating changes in state functions, we will make extensive use
of partial derivatives, which are reviewed in the Math Supplement (Appendix A). The fol-
lowing discussion does not apply to path functions such as w and q because a functional

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