Modern Engineering Thermodynamics

11.7 Constructing Tables and Charts 379
Curve fit 2: p = pðv, TÞðfor superheated and saturated vaporÞ
Curve fit 3: v f = v f ðT sat Þ
Curve fit 4: c 0 v = c0 v ðTÞðfor superheated and saturated vaporÞ (11.31d)
(11.31b)
(11.31c)
C. If a very low-pressure reference state (p 0 , v 0 , T 0 ) is chosen such that ðc v Þ 0 = c 0 v , then Eqs. (11.19), (3.17), and
(11.24) are used to calculate values for u, h, and s relative to this reference state as
Z T Z v
u = u 0 + c 0 v dT + T ∂p
T 0 v 0
∂T
− p
v
dv (11.32)
h = u + pv (3.17)
and
s = s 0 +
Z T
T 0
c 0
v
dT +
T
Z v
v 0
∂p
∂T
dv (11.33)
v
where u 0 and s 0 are the internal energy and entropy values of the reference state. Note that these reference
state properties always cancel out in a typical internal energy change (u 2 – u 1 ) or entropy change (s 2 – s 1 )
calculation, so their values can be arbitrarily chosen and need not be made known to the user of the table
or chart. Typically u 0 and s 0 are chosen so as to make h f and s f zero at the reference temperature T 0 , and T 0 is
often taken to be the triple point temperature (see, for example, the first row of values for water in Table C.1a),
because the triple point is a well-defined and easily reproducible reference state. Therefore, u 0 and s 0 are seldom
chosen to be zero themselves. The generation of the tables can now be carried out as follows.
11.7.1 Saturation tables
A temperature entry saturation table can be constructed as follows:
1. A temperature T = T sat is chosen at which the properties are to be determined.
2. Next, p sat is calculated from Eq. (11.31a).
3. Equation (11.31b), which must be valid for saturated vapor as well as superheated vapor, is used to
calculate v g at these p sat and T sat values.
4. Chose a reference temperature T o and assign arbitrary values to u o and s o .
5. The expression for (dp/dT) sat is determined by differentiating Eq. (11.31a). 3 The values of u g , h g , and s g are
then calculated from Eqs. (11.32), (3.17), and (11.33) by setting (∂p/∂T) v = (dp/dT) sat .
6. Equation (11.31c) is used to calculate v fg = v g – v f at the T sat value.
7. The remaining saturated liquid properties are determined from the Clapeyron and Gibbs Eqs. (11.17) and
(11.10) as follows:
dp
h f = h g − h fg = h g − T sat v fg
dT
and
sat
u f = u g − u fg = u g − ðh fg − p sat v fg Þ
s f = s g − s fg = s g − h fg /T sat
This sequence of operations is repeated for a variety of T sat values, and the compilation of all these results
gives a temperature entry saturation table like Table C.1a or C.1b in Thermodynamic Tables to accompany
Modern Engineering Thermodynamics.
Beginning the calculation sequence with a p = p sat value and calculating the corresponding T sat value
from Eq. (11.31a) and continuing as just described produces a pressure entry saturation table like
Table C.2a or C.2b.
3 Note that Eq. (11.31b) should yield the same values of p sat and T sat as Eq (11.31a). However, they both are both empirical equations
and may not yield the same values of (dp/dT) sat . In this case, Eq. (11.31a) is preferable.