Page 250 - Standard Handbook Of Petroleum & Natural Gas Engineering

Thermodynamics 223

Summary of Thermodynamic Equations

The thermodynamic relations formulated earlier for a pure substance are summarized
in Table 2-19 with unit mass of fluid as the basis. Several additional important relationships
can be derived from them and these are shown in the third column of Table 2-19.
By mathematical manipulation, numerous additional relationships can be
derived from those given in Table 2-19. Of particular significance are expressions
that relate enthalpy H and internal energy U to the measurable variables, P, V,
and T. Thus, choosing the basis as one pound mass,

(2-150)

and
(s)T V (2-151)

-P+.(%)
=

Equations 2-150 and 2-151 apply to any substance or system and are called equations
of state because they completely determine the state of a system in terms of its
thermodynamic properties.

Thermal Properties for Selected Systems
For practical applications of the numerous thermodynamic relationships, it is
necessary to have available the properties of the system. In general, a given property
of a pure substance can be expressed in terms of any other two properties to completely
define the state of the substance. Thus one can represent an equation of state by the
functional relationship:

P = f(T, V) (2-152)

which indicates that the pressure is a function of the temperature and specific volume.
Plots of the properties of various substances as well as tables and charts are extremely
useful in solving engineering thermodynamic problems. Two-dimensional represen-
tations of processes on P-V, T-S, or H-S diagrams are especially useful in analyzing
cyclical processes. The use of the P-V diagram was illustrated earlier. A typical T-S
diagram for a Kankine vapor power cycle is depicted in Figure 2-36.
For the Rankine cycle, the area enclosed by the line segments connecting points
1, 2, 3, 4, 1 on Figure 2-36 represents the net heat transferred into the system per
unit mass, because

s,
Q,,, = js4 dS - I" S (2-158)
T
Td
s>
(lex1 continues on page 226)