def _Ice(T, P):
"""Basic equation for Ice Ih
>>> "%.9f" % _Ice(100,100)["rho"]
'941.678203297'
>>> "%.9f" % _Ice(100,100)["h"]
'-483.491635676'
>>> "%.11f" % _Ice(100,100)["s"]
'-2.61195122589'
>>> "%.11f" % _Ice(273.152519,0.101325)["a"]
'-0.00918701567'
>>> "%.9f" % _Ice(273.152519,0.101325)["u"]
'-333.465403393'
>>> "%.11f" % _Ice(273.152519,0.101325)["cp"]
'2.09671391024'
>>> "%.15f" % _Ice(273.16,611.657e-6)["alfav"]
'0.000159863102566'
>>> "%.11f" % _Ice(273.16,611.657e-6)["beta"]
'1.35714764659'
>>> "%.11e" % _Ice(273.16,611.657e-6)["kt"]
'1.17793449348e-04'
>>> "%.11e" % _Ice(273.16,611.657e-6)["ks"]
'1.14161597779e-04'
"""
# Check input in range of validity
if P < Pt:
Psub = _Sublimation_Pressure(T)
if Psub > P:
# Zone Gas
raise NotImplementedError("Incoming out of bound")
elif P > 208.566:
# Ice Ih limit upper pressure
raise NotImplementedError("Incoming out of bound")
else:
Pmel = _Melting_Pressure(T, P)
if Pmel < P:
# Zone Liquid
raise NotImplementedError("Incoming out of bound")
Tr = T/Tt
Pr = P/Pt
P0 = 101325e-6/Pt
s0 = -0.332733756492168e4*1e-3 # Express in kJ/kgK
gok = [-0.632020233335886e6, 0.655022213658955, -0.189369929326131e-7,
0.339746123271053e-14, -0.556464869058991e-21]
r2k = [complex(-0.725974574329220e2, -0.781008427112870e2)*1e-3,
complex(-0.557107698030123e-4, 0.464578634580806e-4)*1e-3,
complex(0.234801409215913e-10, -0.285651142904972e-10)*1e-3]
t1 = complex(0.368017112855051e-1, 0.510878114959572e-1)
t2 = complex(0.337315741065416, 0.335449415919309)
r1 = complex(0.447050716285388e2, 0.656876847463481e2)*1e-3
go = gop = gopp = 0
for k in range(5):
go += gok[k]*1e-3*(Pr-P0)**k
for k in range(1, 5):
gop += gok[k]*1e-3*k/Pt*(Pr-P0)**(k-1)
for k in range(2, 5):
gopp += gok[k]*1e-3*k*(k-1)/Pt**2*(Pr-P0)**(k-2)
r2 = r2p = 0
for k in range(3):
r2 += r2k[k]*(Pr-P0)**k
for k in range(1, 3):
r2p += r2k[k]*k/Pt*(Pr-P0)**(k-1)
r2pp = r2k[2]*2/Pt**2
c = r1*((t1-Tr)*log_c(t1-Tr)+(t1+Tr)*log_c(t1+Tr)-2*t1*log_c(
t1)-Tr**2/t1)+r2*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ct = r1*(-log_c(t1-Tr)+log_c(t1+Tr)-2*Tr/t1)+r2*(
-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
ctt = r1*(1/(t1-Tr)+1/(t1+Tr)-2/t1) + r2*(1/(t2-Tr)+1/(t2+Tr)-2/t2)
cp = r2p*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ctp = r2p*(-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
cpp = r2pp*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
g = go-s0*Tt*Tr+Tt*c.real
gt = -s0+ct.real
gp = gop+Tt*cp.real
gtt = ctt.real/Tt
gtp = ctp.real
gpp = gopp+Tt*cpp.real
propiedades = {}
propiedades["gt"] = gt
propiedades["gp"] = gp
propiedades["gtt"] = gtt
propiedades["gpp"] = gpp
propiedades["gtp"] = gtp
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = gp/1000
propiedades["rho"] = 1000./gp
propiedades["h"] = g-T*gt
propiedades["s"] = -gt
propiedades["cp"] = -T*gtt
propiedades["u"] = g-T*gt-P*gp
propiedades["g"] = g
propiedades["a"] = g-P*gp
propiedades["alfav"] = gtp/gp
propiedades["beta"] = -gtp/gpp
propiedades["kt"] = -gpp/gp
propiedades["ks"] = (gtp**2-gtt*gpp)/gp/gtt
return propiedades
def _Ice(T, P):
"""Basic state equation for Ice Ih
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties of ice. The available properties are:
* rho: Density, [kg/m³]
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* alfav: Cubic expansion coefficient, [1/K]
* beta: Pressure coefficient, [MPa/K]
* xkappa: Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* gt: [∂g/∂T]P
* gtt: [∂²g/∂T²]P
* gp: [∂g/∂P]T
* gpp: [∂²g/∂P²]T
* gtp: [∂²g/∂T∂P]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* T ≤ 273.16
* P ≤ 208.566
* State below the melting and sublimation lines
Examples
--------
>>> st1 = _Ice(100, 100)
>>> st1["rho"], st1["h"], st1["s"]
941.678203297 -483.491635676 -2.61195122589
>>> st2 = _Ice(273.152519,0.101325)
>>> st2["a"], st2["u"], st2["cp"]
-0.00918701567 -333.465403393 2.09671391024
>>> st3 = _Ice(273.16,611.657e-6)
>>> st3["alfav"], st3["beta"], st3["xkappa"], st3["ks"]
0.000159863102566 1.35714764659 1.17793449348e-04 1.14161597779e-04
References
----------
IAPWS, Revised Release on the Equation of State 2006 for H2O Ice Ih
September 2009, http://iapws.org/relguide/Ice-2009.html
"""
# Check input in range of validity
if T > 273.16:
# No Ice Ih stable
warnings.warn("Metastable ice")
elif P > 208.566:
# Ice Ih limit upper pressure
raise NotImplementedError("Incoming out of bound")
elif P < Pt:
Psub = _Sublimation_Pressure(T)
if Psub > P:
# Zone Gas
warnings.warn("Metastable ice in vapor region")
elif 251.165 < T:
Pmel = _Melting_Pressure(T)
if Pmel < P:
# Zone Liquid
warnings.warn("Metastable ice in liquid region")
Tr = T/Tt
Pr = P/Pt
P0 = 101325e-6/Pt
s0 = -0.332733756492168e4*1e-3 # Express in kJ/kgK
gok = [-0.632020233335886e6, 0.655022213658955, -0.189369929326131e-7,
0.339746123271053e-14, -0.556464869058991e-21]
r2k = [complex(-0.725974574329220e2, -0.781008427112870e2)*1e-3,
complex(-0.557107698030123e-4, 0.464578634580806e-4)*1e-3,
complex(0.234801409215913e-10, -0.285651142904972e-10)*1e-3]
t1 = complex(0.368017112855051e-1, 0.510878114959572e-1)
t2 = complex(0.337315741065416, 0.335449415919309)
r1 = complex(0.447050716285388e2, 0.656876847463481e2)*1e-3
go = gop = gopp = 0
for k in range(5):
go += gok[k]*1e-3*(Pr-P0)**k
for k in range(1, 5):
gop += gok[k]*1e-3*k/Pt*(Pr-P0)**(k-1)
for k in range(2, 5):
gopp += gok[k]*1e-3*k*(k-1)/Pt**2*(Pr-P0)**(k-2)
r2 = r2p = 0
for k in range(3):
r2 += r2k[k]*(Pr-P0)**k
for k in range(1, 3):
r2p += r2k[k]*k/Pt*(Pr-P0)**(k-1)
r2pp = r2k[2]*2/Pt**2
c = r1*((t1-Tr)*log_c(t1-Tr)+(t1+Tr)*log_c(t1+Tr)-2*t1*log_c(
t1)-Tr**2/t1)+r2*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ct = r1*(-log_c(t1-Tr)+log_c(t1+Tr)-2*Tr/t1)+r2*(
-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
ctt = r1*(1/(t1-Tr)+1/(t1+Tr)-2/t1) + r2*(1/(t2-Tr)+1/(t2+Tr)-2/t2)
cp = r2p*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ctp = r2p*(-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
cpp = r2pp*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
g = go-s0*Tt*Tr+Tt*c.real
gt = -s0+ct.real
gp = gop+Tt*cp.real
gtt = ctt.real/Tt
gtp = ctp.real
gpp = gopp+Tt*cpp.real
propiedades = {}
propiedades["gt"] = gt
propiedades["gp"] = gp
propiedades["gtt"] = gtt
propiedades["gpp"] = gpp
propiedades["gtp"] = gtp
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = gp/1000
propiedades["rho"] = 1000./gp
propiedades["h"] = g-T*gt
propiedades["s"] = -gt
propiedades["cp"] = -T*gtt
propiedades["u"] = g-T*gt-P*gp
propiedades["g"] = g
propiedades["a"] = g-P*gp
propiedades["alfav"] = gtp/gp
propiedades["beta"] = -gtp/gpp
propiedades["xkappa"] = -gpp/gp
propiedades["ks"] = (gtp**2-gtt*gpp)/gp/gtt
return propiedades
def _Ice(T, P):
"""Basic equation for Ice Ih
>>> "%.9f" % _Ice(100,100)["rho"]
'941.678203297'
>>> "%.9f" % _Ice(100,100)["h"]
'-483.491635676'
>>> "%.11f" % _Ice(100,100)["s"]
'-2.61195122589'
>>> "%.11f" % _Ice(273.152519,0.101325)["a"]
'-0.00918701567'
>>> "%.9f" % _Ice(273.152519,0.101325)["u"]
'-333.465403393'
>>> "%.11f" % _Ice(273.152519,0.101325)["cp"]
'2.09671391024'
>>> "%.15f" % _Ice(273.16,611.657e-6)["alfav"]
'0.000159863102566'
>>> "%.11f" % _Ice(273.16,611.657e-6)["beta"]
'1.35714764659'
>>> "%.11e" % _Ice(273.16,611.657e-6)["kt"]
'1.17793449348e-04'
>>> "%.11e" % _Ice(273.16,611.657e-6)["ks"]
'1.14161597779e-04'
"""
# Check input in range of validity
if P < Pt:
Psub = _Sublimation_Pressure(T)
if Psub > P:
# Zone Gas
raise NotImplementedError("Incoming out of bound")
elif P > 208.566:
# Ice Ih limit upper pressure
raise NotImplementedError("Incoming out of bound")
else:
Pmel = _Melting_Pressure(T, P)
if Pmel < P:
# Zone Liquid
raise NotImplementedError("Incoming out of bound")
Tr = T/Tt
Pr = P/Pt
P0 = 101325e-6/Pt
s0 = -0.332733756492168e4*1e-3 # Express in kJ/kgK
gok = [-0.632020233335886e6, 0.655022213658955, -0.189369929326131e-7,
0.339746123271053e-14, -0.556464869058991e-21]
r2k = [complex(-0.725974574329220e2, -0.781008427112870e2)*1e-3,
complex(-0.557107698030123e-4, 0.464578634580806e-4)*1e-3,
complex(0.234801409215913e-10, -0.285651142904972e-10)*1e-3]
t1 = complex(0.368017112855051e-1, 0.510878114959572e-1)
t2 = complex(0.337315741065416, 0.335449415919309)
r1 = complex(0.447050716285388e2, 0.656876847463481e2)*1e-3
go = gop = gopp = 0
for k in range(5):
go += gok[k]*1e-3*(Pr-P0)**k
for k in range(1, 5):
gop += gok[k]*1e-3*k/Pt*(Pr-P0)**(k-1)
for k in range(2, 5):
gopp += gok[k]*1e-3*k*(k-1)/Pt**2*(Pr-P0)**(k-2)
r2 = r2p = 0
for k in range(3):
r2 += r2k[k]*(Pr-P0)**k
for k in range(1, 3):
r2p += r2k[k]*k/Pt*(Pr-P0)**(k-1)
r2pp = r2k[2]*2/Pt**2
c = r1*((t1-Tr)*log_c(t1-Tr)+(t1+Tr)*log_c(t1+Tr)-2*t1*log_c(t1)-Tr**2/t1) + \
r2*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ct = r1*(-log_c(t1-Tr)+log_c(t1+Tr)-2*Tr/t1) + \
r2*(-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
ctt = r1*(1/(t1-Tr)+1/(t1+Tr)-2/t1) + r2*(1/(t2-Tr)+1/(t2+Tr)-2/t2)
cp = r2p*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ctp = r2p*(-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
cpp = r2pp*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
g = go-s0*Tt*Tr+Tt*c.real
gt = -s0+ct.real
gp = gop+Tt*cp.real
gtt = ctt.real/Tt
gtp = ctp.real
gpp = gopp+Tt*cpp.real
propiedades = {}
propiedades["gt"] = gt
propiedades["gp"] = gp
propiedades["gtt"] = gtt
propiedades["gpp"] = gpp
propiedades["gtp"] = gtp
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = gp/1000
propiedades["rho"] = 1000./gp
propiedades["h"] = g-T*gt
propiedades["s"] = -gt
propiedades["cp"] = -T*gtt
propiedades["u"] = g-T*gt-P*gp
propiedades["g"] = g
propiedades["a"] = g-P*gp
propiedades["alfav"] = gtp/gp
propiedades["beta"] = -gtp/gpp
propiedades["kt"] = -gpp/gp
propiedades["ks"] = (gtp**2-gtt*gpp)/gp/gtt
return propiedades