Modern Engineering Thermodynamics

404 CHAPTER 11: More Thermodynamic Relations
Make your percent error calculations here at 20.0°F intervals
between 40.0 and 700.°F.
c. By 1899, very careful p sat – T sat measurements had been
made, and K. Thiesen curve fit these data to the following
equation:
ðT sat +459:6Þlog 10 p sat = 5:409ðT sat −212Þ
−ð8:71×10 −10 Þ ð689−T sat Þ 4 −ð477Þ 4
where p sat is in atmospheres and T sat is in °F. Make your
percent error calculations here at intervals of 20.0°F between
20.0 and 700.°F.
d. By 1915, G. A. Goodenough had developed the following
more complex equation, which he claimed fit steam quite
well over the entire range from 32.0°F to the critical point
(705°F).
log 10 p sat = A − B/T sat − Clog 10 T sat − DT sat + ET 2 sat − F
where F = 0.0002{10 – 10[(T sat – 829.6)/100] 2 +
[(T sat – 829.6)/100] 4 }. Here, p sat is in psia, T sat is in R,
and
A = 10:5688080 log 10 D = 7:6088020 − 10
log 10 B = 3:6881209 log 10 E = 4:1463000 − 10
C = 0:0155
Make your percent error calculations at any convenient
temperature interval between 32.0 and 705°F. Note: The use
of base 10 logarithms in these equations is the way these
equations were originally written, and it has been continued
here for historical accuracy.
87.* Equations (11.31) for mercury are given by
1. ln p sat = 23.6321 − 7042.6208/T sat − 0.1207 (ln T sat )
− 58,060.290/T 2 sat.
2. p = RT/v − (T/v 2 ) exp[10.3338 − 312.0954/T − 2.0795
(ln T)].
3. v f = [12,813.6070 − 2.4531(T sat − 600)−0.000267(T sat − 600) 2 ] −1 .
4. c v ° = 62.168 J/(kg·K) = constant.
where p and p sat are in Pa, T and T sat are in K, and v and v f
are in m 3 /kg, and R = 41.4453 J/(kg· K). Develop a
computer spreadsheet that returns v, u, h, ands values when
p and T are input. Make sure your program checks to see
what region (saturated or superheated) your input data are
in. For T sat =750.K,youshouldgeth fg =291kJ/kgands fg =
0.388 kJ/kg. These values are independent of your reference
state values. Note: More ambitious programs can now be
produced by adding subroutines that return the remaining
properties when any pair of independent properties (T-s, p-h,
etc.) are input.