Page 237 - Standard Handbook Of Petroleum & Natural Gas Engineering

210 General Engineering and Science

P = absolute pressure, Ib,/ft2
Pq = entropy production rate, Btu/”R*s
Q= heat transferred to system across a system boundary, Btu/lb, or Btu
Q = rate of heat transfer, Btu/s
R = universal gas constant, lb,-ftg/mole*”R
s, S = entropy, Btu/lbmoR or Btu/”R
T = absolute temperature, “R
u, U = internal energy, Btu/lb, or Btu
V = volume, ft’/lb, or ft’
v = flow velocity, ft/s
W = work done by a system against its surroundings, Btu/lb, or Btu
Z = height from center of gravity of a fluid mass to a fixed base level, ft
The First Law of Thermodynamics

The differrential form of the first law as applied to a closed system, for which there
is no exchange of matter between the system and its surroundings, is given by
dU = SQ - 6W (2-102)
where dU represents an infinitesimal increase in the internal energy of the system,
6Q is the heat absorbed by the system from its surroundings, and 6W is the work
done by the system on its surroundings. The state of a system is defined by its
temperature, pressure, specific volume, and chemical composition. The change in
internal energy expressed by Equation 2-102 depends only upon the difference between
the final and initial states and not upon the process or processes that occurred during
the change. The heat and work terms, on the other hand, are dependent upon the
process path. For a change from a state A to a state B, the first law becomes
AU=U,- U,=Q- W (2-103)
Work interchange between a system and its surroundings can take on any of a variety
of forms including mechanical shaft work, electrical work, magnetic work, surface tension,
etc. For many applications, the only work involved is that of compression or expansion
against the surroundings, in which case the work term in Equation 2-102 becomes
6W = PdV
or
W = I’”
P
dV
”a (2-104)
where V, is the final volume and V, the initial volume of the system, and P is the
system pressure. Thus, for a constant pressure process:
W = PAV = P(V, - V,) (constant pressure process) (2-105)
or, combining Equations 2-103 and 2-104:
AU =U, - U, = Q- PV, + PV, (2- 106)
or
Q (U, + PV,) - (U, + PV,) (2-107)
The combination of properties (U + PV) occurs so frequently in thermodynamics
that it is given a special symbol, H, and termed the “enthalpy” or “heat content” of
the system. Thus Equation 2-107 can be written as