Fluid Properties in Calcumber

Example

Power Required for Superheated Steam Production

Heating water requires energy, but most of the energy is needed for the phase change from liquid water to steam. What power is required to convert 1 litre of water per hour at 20 °C into steam at 160 °C for industrial process heat?

Expression Result
load fluid water 1
   
Enthalpy of water and steam:  
h1 = h(1 bar, 20 °C) 84.006054 kJ/kg
h2 = h(4 bar, 160 °C) 2775.1891 kJ/kg
   
Water flow:        Vt   = 1 L/h 1 L/h
Density of water:  rho1 = rho(1 bar, 20 °C) 998.20654 kg/m3
mass flow:         mt   = Vt*rho1 to kg/h 0.99820654 kg/h
Heat flow:         Qt   = (h2 - h1) * mt 746.21016 W

Loading Fluids

Fluids can be loaded using the load fluid command. The result value indicates whether the fluid was loaded (1) or not (0). The command directly defines the functions p(a, b), h(a, b), .... Any existing function with the same name is overridden.

To use multiple fluids, use the as statement to define aliases for each fluid. The alias is then used as prefix and postfix to define the function names.

Expression Result
load fluid air 1
rho(1 bar, 20 °C) 1.1888175 kg/m3
h(10 MPa, 500 K) 625.57961 kJ/kg
   
load fluid nitrogen as N 1
N_rho(1 bar, 20 °C) 1.1495944 kg/m3
rho_N(1 bar, 20 °C) 1.1495944 kg/m3
   
load fluid chocolate 0

Find the list of available pure fluids and fluid mixtures in the Reference.

Defining States, Calculating Properties

Input Properties

Typically, the state of a fluid is fully defined by a known pair of properties.
Use a pair of the following properties to define a state:

For a defined state, you can then query different kind of properties as shown below. The sequence in which you pass the arguments to the function does not play a role. Calcumber identifies the type of the parameters by its unit.

Expression Result
load fluid water 1
   
Define state:  
T = 20 °C 20 °C
p = 1 bar 1 bar
   
Query properties:  
rho(T, p) 998.20654 kg/m3
s(T, p) 0.29646311 kJ/(kg*K)
h(T, p) 84.006054 kJ/kg
   
Directly pass values for p and h:  
x(950 hPa, 1500 kJ/kg) to % 48.138810 %

More State Properties

In addition to the properties defined above (p, T, h, s, rho and x), there are more properties as listed below. The values of these properties can be calculated from a defined state, but these properties cannot be used to define states.

load fluid ethanol 1
T = -5 °C -5 °C
p = 0.5 bar 0.5 bar
   
Gibbs energy:          g(T,p) -28.689770 kJ/kg
Internal energy:       u(T,p) -212.54646 kJ/kg
Specific volume:       v(T,p) 0.0012336460 m3/kg
Speed of sound:        a(T,p) 1246.8739 m/s
Viscosity:             mu(T,p) to mPa*s 2.0357303 mPa*s
Thermal conductivity:  k(T,p) 0.17013680 W/(m*K)
Surface tension:       sigma(T) 0.024772133 N/m
   
Specific heat:  
at constant pressure: cp(T, p) 2226.0719 J/(kg*K)
at constant volume:   cv(T, p) 1848.7873 J/(kg*K)

Two Phase Region

For a pure fluid, saturation pressure and saturation temperature are uniquely related. Therefore p(T) and T(p) can be used to calculate the saturation pressure or temperature. The vapor quality does not affect the result. For mixed fluids, these functions return the values at 50% vapor quality.

Expression Result
load fluid nitrogen 1
   
In two phase region:  
   
Saturation temperature from pressure: T(1 bar) 77.243500 K
Saturation pressure from temperature: p(100 K) 7.7827498 bar
   
Enthalpy at bubble and dew point:  
p = 1 bar 1 bar
h_bubble = h(p, 0%) -122.24684 kJ/kg
h_mix    = h(p, 90%) 57.140879 kJ/kg
h_dew    = h(p, 100%) 77.072847 kJ/kg
   
Enthalpy values may be positive or negative  
because the enthalpy reference point is arbitrary.  
Only enthalpy differences are physically meaningful.  
   
Enthalpy of vaporization:  
h_vap = h_dew - h_bubble 199.31969 kJ/kg

State Independent Properties

Expression Result
load fluid R11 1
   
Critical temperature: T_crit 471.11 K
   
Triple point:  
p_triple 0.000065100898 bar
T_triple 162.68 K
   
Molar mass: M 137.368 g/mol
   
Global warming potential:  
GWP20 6730
GWP100 4750
GWP500 1620
   
Ozone depletion potential:  
ODP 1

Temperature Conversion

The following temperature units are defined in Calcumber:

K Kelvin. Base unit for all temperatures.
°C or degC Degree Celsius
°F or degF Degree Fahrenheit
°Ra or degRa Degree Rankine

By default, all temperature values are interpreted as temperature differences. Therefore, converting °C to Kelvin will not add 273.15 K. This behavior prevents interpretation problems in many calculations as shown in the example below:

Expression Result
Mass:           m  = 100 kg 100 kg
Temp. increase: ΔT = 40 °C 40 °C
Spec. heat:     cp = 4182 J/(kg*K) 4182 J/(kg*K)
   
Energy needed:  
m * ΔT * cp  to kWh 4.6466667 kWh

Heating up 100 kg of water by 40°C needs 4.6 kWh. If Calcumber would convert 40°C to 313 K, the result would be 36.4 kWh, which would be the value for heating it up from 0 K to 313 K.

For converting actual temperature values between the scales, use the defined conversion functions as below:

Expression Result
Conversion of temperature differences:  
10 °C  to K 10 K
10 °F  to K 5.5555556 K
   
Conversion of temperature values:  
to_K(10 °C) 283.15 K
to_K(10 °F) 260.92778 K
to_degF(0 °C) 32 °F
to_degC(0 °F) -17.777778 °C
to_degRa(1000 °C) 2291.67 °Ra

Refrigeration Cycle Example

This example calculates a simple vapor-compression refrigeration cycle using propane (R290) as the refrigerant.

Starting from the evaporation and condensation temperature, superheating, subcooling, and compressor isentropic efficiency, Calcumber calculates the thermodynamic state at each point of the cycle. The required fluid properties such as pressure, enthalpy, entropy, and specific volume are obtained directly from the integrated CoolProp thermodynamic property library. The example then determines the coefficient of performance (COP), compressor power consumption, refrigerant mass flow rate, and suction volume flow required to deliver a heating capacity of 10 kW.

Click the table to open the calculation in Calcumber. You can modify the temperatures, refrigerant, efficiency, or heating capacity and immediately see how the cycle performance changes.

load fluid R290 1
   
Evaporation temperature:     T_v = -10 °C -10 °C
Condensation temperature:    T_k = 45 °C 45 °C
Subcooling:                  T_sc = 5 °C 5 °C
Superheating:                T_sh = 10 °C 10 °C
Isentropic efficiency:       eff = 60 % 60 %
Heating capacity:            Qt_h = 10 kW 10 kW
   
Evaporation pressure:    p_v = p(T_v) 3.4527994 bar
Condensation pressure:   p_k = p(T_k) 15.343141 bar
   
Before compression:  
T1 = T_v + T_sh 0 °C
h1 = h(T1, p_v) 580.29472 kJ/kg
s1 = s(T1, p_v) 2.4466331 kJ/(kg*K)
v1 = v(T1, p_v) 0.13762839 m3/kg
   
Compression:  
h2s = h(s1, p_k) 654.16499 kJ/kg
h2 = h1 + (h2s - h1)/eff  to kJ/kg 703.41183 kJ/kg
T2 = T(h2, p_k) 356.25538 K
   
Subcooling:  
h3 = h(p_k, T_k - T_sc) 307.05278 kJ/kg
   
Expansion:  
h4 = h3 307.05278 kJ/kg
   
COP, Power, Mass Flow Rate  
==========================  
COP = (h2 - h3)/(h2 - h1) 3.2193661
P_el = Qt_h / COP 3.1062015 kW
mt = Qt_h / (h2 - h3) to g/s 25.229649 g/s
Vt = v1 * mt  to m3/h 12.500338 m3/h

Example with Multiple Fluids

This example demonstrates how multiple fluids can be used within the same Calcumber calculation. Water is loaded as `fluid1` and air as `fluid2`, allowing thermodynamic properties of both fluids to be accessed independently.

The first part calculates the heating power transferred by a hydronic heating circuit from the supply and return temperatures, pressure, and water flow rate. The second part models the air side of an air-to-water heat pump. Using the calculated heating power and the airflow rate, it determines the enthalpy and temperature drop of the air as heat is extracted from the source.

This approach is useful whenever energy is transferred between different media, such as water and air, water and refrigerant, or refrigerant and air. By assigning each fluid its own name, properties from multiple fluids can be combined in a single calculation.

load fluid water as fluid1 1
load fluid air as fluid2 1
   
Heating Circuit  
===============  
Flow rate:            Vt = 10 l/min 10 l/min
Supply temperature:  T_s = 32 °C 32 °C
Return temperature:  T_r = 24 °C 24 °C
Pressure:              p = 3 bar 3 bar
   
Power:  
Δh = fluid1_h(p, T_s) - fluid1_h(p, T_r) 33.438783 kJ/kg
P = Δh * fluid1_rho(p, T_s) * Vt to kW 5.5459130 kW
   
Source, Air-to-Water Heat Pump  
==============================  
Volume flow rate:   Vt_L = 2400 m3/h 2400 m3/h
Inlet temperature:  T_in = 2 °C 2 °C
Mass flow rate:     m_t = fluid2_rho(T_in, 1 bar) * Vt_L 3040.4126 kg/h
   
Calculation of Cooling  
======================  
Specific enthalpy of inlet air:  
h_in = fluid2_h(T_in, 1 bar) 401.30214 kJ/kg
   
Specific enthalpy of outlet air:  
h_out = h_in - P / m_t 394735.50 m2/s2
   
Outlet air temperature:  
T_out = fluid2_T(1 bar, h_out) 268.62020 K
In °C: to_degC(T_out) -4.5298048 °C

Reference

Pure Fluids List

List of available fluids with aliases.
Fluid Aliases
1-Butene 1Butene, 1BUTENE, 1-BUTENE, Butene
Acetone acetone, ACETONE
Air air, AIR, R729
Ammonia NH3, ammonia, R717, AMMONIA
Argon argon, ARGON, R740, Ar
Benzene benzene, BENZENE
CarbonDioxide R744, co2, CO2, carbondioxide, CARBONDIOXIDE
CarbonMonoxide CO, CARBONMONOXIDE
CarbonylSulfide COS, CARBONYLSULFIDE
cis-2-Butene Cis-2-Butene, CIS-2-BUTENE, C2BUTENE
CycloHexane Cyclohexane, CYCLOHEXANE, CYCLOHEX
Cyclopentane CycloPentane, cyclopentane, CYCLOPENTANE, CYCLOPEN
CycloPropane cyclopropane, Cyclopropane, CYCLOPROPANE, CYCLOPRO
D4 Octamethylcyclotetrasiloxane, OCTAMETHYLCYCLOTETRASILOXANE
D5 Decamethylcyclopentasiloxane, DECAMETHYLCYCLOPENTASILOXANE
D6 Dodecamethylcyclohexasiloxane, DODECAMETHYLCYCLOHEXASILOXANE
Deuterium deuterium, DEUTERIUM, D2
Dichloroethane DICHLOROETHANE, 1, 2-dichloroethane, 1, 2-DICHLOROETHANE
DiethylEther DEE, DiethylEther
DimethylCarbonate DMC, dimethylcarbonate, DIMETHYLCARBONATE
DimethylEther DIMETHYLETHER, DME
Ethane ethane, ETHANE, R170, n-C2H6
Ethanol C2H6O, ethanol, ETHANOL
EthylBenzene ethylbenzene, ETHYLBENZENE, EBENZENE
Ethylene ethylene, ETHYLENE, R1150
EthyleneOxide ETHYLENEOXIDE
Fluorine fluorine, FLUORINE
HeavyWater D2O, HEAVYWATER
Helium helium, HELIUM, He, R704
HFE143m HFE-143m, HFE143M, HFE-143M, RE143A, RE143a
Hydrogen hydrogen, HYDROGEN, H2, R702
HydrogenChloride HydrogenChloride, HYDROGENCHLORIDE, HCl, HCL
HydrogenSulfide H2S, HYDROGENSULFIDE
IsoButane isobutane, Isobutane, ISOBUTANE, R600A, R600a, ISOBUTAN
IsoButene Isobutene, ISOBUTENE, IBUTENE
Isohexane ihexane, ISOHEXANE
Isopentane ipentane, R601a, ISOPENTANE, IPENTANE
Krypton krypton, KRYPTON
m-Xylene mXylene, m-xylene, M-XYLENE, MC8H10
MD2M Decamethyltetrasiloxane, DECAMETHYLTETRASILOXANE
MD3M Dodecamethylpentasiloxane, DODECAMETHYLPENTASILOXANE
MD4M Tetradecamethylhexasiloxane, TETRADECAMETHYLHEXASILOXANE
MDM Octamethyltrisiloxane, OCTAMETHYLTRISILOXANE
Methane CH4, methane, METHANE, R50, n-C1H4
Methanol methanol, METHANOL
MethylLinoleate METHYLLINOLEATE, MLINOLEA
MethylLinolenate METHYLLINOLENATE, MLINOLEN
MethylOleate METHYLOLEATE, MOLEATE
MethylPalmitate METHYLPALMITATE, MPALMITA
MethylStearate METHYLSTEARATE, MSTEARAT
MM Hexamethyldisiloxane, HEXAMETHYLDISILOXANE
n-Butane nButane, butane, Butane, BUTANE, N-BUTANE, R600, NC4H10, n-C4H10
n-Decane Decane, decane, DECANE, N-DECANE, NC10H22, n-C10H22
n-Dodecane nDodecane, Dodecane, DODECANE, N-DODECANE, C12, NC12H26, n-C12H26
n-Heptane nHeptane, Heptane, HEPTANE, N-HEPTANE, NC7H16, n-C7H16
n-Hexane nHexane, Hexane, HEXANE, N-HEXANE, NC6H14, n-C6H14
n-Nonane nonane, Nonane, NONANE, N-NONANE, NC9H20, n-C9H20
n-Octane nOctane, Octane, OCTANE, N-OCTANE, NC8H18, n-C8H18
n-Pentane nPentane, Pentane, PENTANE, N-PENTANE, R601, NC5H12, n-C5H12
n-Propane Propane, propane, R290, C3H8, PROPANE, N-PROPANE, NC3H8, n-C3H8
n-Undecane Undecane, UNDECANE, N-UNDECANE, C11, NC11H24, n-C11H24
Neon neon, NEON, R720
Neopentane neopentn, NEOPENTANE
Nitrogen nitrogen, NITROGEN, N2, R728
NitrousOxide N2O, NITROUSOXIDE
Novec649 Novec1230, NOVEC649
o-Xylene oXylene, o-xylene, O-XYLENE, OC8H10
OrthoDeuterium orthodeuterium, ORTHODEUTERIUM
OrthoHydrogen Orthohydrogen, orthohydrogen, ORTHOHYDROGEN, ORTHOHYD
Oxygen oxygen, OXYGEN, O2, R732
p-Xylene pXylene, p-xylene, P-XYLENE, PC8H10
ParaDeuterium paradeuterium, PARADEUTERIUM
ParaHydrogen Parahydrogen, parahydrogen, PARAHYDROGEN, PARAHYD
Propylene propylene, PROPYLENE, PROPYLEN, R1270
Propyne propyne, PROPYNE
R11
R113
R114
R115
R116
R12
R123
R1233zd(E) R1233zdE, R1233ZDE, R1233ZD(E), R1233ZD
R1234yf R1234YF
R1234ze(E) R1234ZE, R1234ZEE, R1234zeE, R1234ZE(E)
R1234ze(Z) R1234ZE(Z), R1234ZEZ
R124
R1243zf R1243ZF
R125
R13
R1336mzz(E) (E)-1, 1, 1, 4, 4, 4-HEXAFLUORO-2-BUTENE, r1336mzz(e), R1336mzz(E), (E)-1, 1, 1, 4, 4, 4-Hexafluoro-2-butene, R1336MZZ(E), (e)-1, 1, 1, 4, 4, 4-hexafluoro-2-butene, R1336MZZE
R134a R134A
R13I1 CF3I
R14
R141b R141B
R142b R142B
R143a R143A
R152A R152a
R161 Fluoroethane, FLUOROETHANE
R21
R218
R22
R227EA R227ea
R23
R236EA R236ea
R236FA R236fa
R245ca R245CA
R245fa R245FA
R32
R365MFC R365mfc
R40 MethylChloride
R404A R404a
R407C R407c
R41
R410A R410a
R507A R507a
RC318
SES36
SulfurDioxide SO2, SULFURDIOXIDE
SulfurHexafluoride SULFURHEXAFLUORIDE, SF6
Toluene toluene, TOLUENE
trans-2-Butene Trans-2-Butene, TRANS-2-BUTENE, T2BUTENE
Water water, WATER, H2O, h2o, R718
Xenon Xe, xenon, XENON

Fluid Mixtures List

Besides pure fluids, there is a list of mixtures that can be loaded:

Air (air, AIR, R729), Amarillo, Ekofisk, GulfCoast, GulfCoastGas(NIST1), HighCO2, HighN2, NaturalGasSample, TypicalNaturalGas

R401A, R401B, R401C, R402A, R402B, R403A, R403B, R404A, R405A, R406A, R407A, R407B, R407C, R407D, R407E, R407F, R408A, R409A, R409B, R410A, R410B, R411A, R411B, R412A, R413A, R414A, R414B, R415A, R415B, R416A, R417A, R417B, R417C, R418A, R419A, R419B, R420A, R421A, R421B, R422A, R422B, R422C, R422D, R422E, R423A, R424A, R425A, R426A, R427A, R428A, R429A, R430A, R431A, R432A, R433A, R433B, R433C, R434A, R435A, R436A, R436B, R437A, R438A, R439A, R440A, R441A, R442A, R443A, R444A, R444B, R445A, R446A, R447A, R448A, R449A, R449B, R450A, R451A, R451B, R452A, R453A, R454A, R454B, R500, R501, R502, R503, R504, R507A, R508A, R508B, R509A, R510A, R511A, R512A, R513A

Phase Diagrams

Calcumber does not currently generate phase diagrams. For plotting thermodynamic cycles and visualizing fluid states, we recommend using CoolPack. Although the software developed in the 90's at the Technical University of Denmark is no longer maintained, it remains a valuable tool and still runs on Windows. For convenience, log(p)-h diagrams for all fluids available in CoolPack have been generated and are provided below as PDF files.

R11, CCl3F Trichlorofuoromethane

R113, CCl2FCClF2, Trichlorotrifluoroethane

R114, CClF2CClF2, Dichlorotetrafluoroethane

R1150, CH2=CH2, Ethene (ethylene]

R12, CCl2F2, Dichlorodifluoromethane

R123, CHCI2CF3, Dichlorotrifluoroethane

R1270, CH3CH=CH2, Propene (propylene)

R13, CClF3, Chlorotrifluoromethane

R134a, CH2FCF3, 1,1,1,2-tetrafluoroethane

R14, CF4, Tetrafluoromethane

R152a, CH3CHF2, 1,1-difluoroethane

R170, CH3CH3, Ethane

R21, CHCI2F, Dichlorofluoromethane

R22, CHCIF2, Chlorodifluoromethane

R23, CHF3, Trifluoromethane

R290, CH3CH2CH3, Propane

R401a, R22/R152a/R124 (53/13/34)

R401b, R22/R152a/R124 (61/11/28)

R401c, R22/R152a/R124 (33/15/52)

R402a, R125/R290/R22 (60/2/38)

R402b, R125/R290/R22 (38/2/60)

R404a, R125/R143a/R134a (44/52/4)

R406a, R22/R142b/R600a (55/41/4)

R407a, R32/R125/R134a (20/40/40)

R407b, R32/R125/R134a (10/70/20)

R407c, R32/R125/R134a (23/25/52)

R408a, R22/143a/R125 (47/46/7)

R409a, R22/R124/R142b (60/25/15)

R410a, R32/R125 (50/50)

R410b, R32/R125 (45/55)

R50, CH4, Methane

R500, R12/R152a (73.8/26.2)

R502, R22/R115 (48.8/51.2)

R507, R125/R143a (50/50)

R508a, R23/R116 (39/61)

R600, CH3CH2CH2CH3, Butane

R600a, CH(CH3)3, 2-methyl propane (isobutane)

R717, NH3, Ammonia

R718, H2O, Water,

R718, H20, Water, high range

R728, N2, Nitrogen

R729, N2/02/A (76/23/1), Air

R732, O2, Oxygen

R740, Ar, Argon

R744, CO2, Carbon dioxide

RC318, C4F8, Octafluorocyclobutane

Credits

CoolPack

Phase diagrams provided here were created using Cool CoolPack. The software was developed in the 1990s at the Technical University of Denmark. Althogh it is no longer maintained, it still runs on Windows and remains a valuabletool for refrigeration and thermodynamic calculations.

You might also be interested in CoolTools, which is intended to become the successor for CoolPack.

CoolProp

Calcumber uses CoolProp to calculate thermodynamic fluid properties. CoolProp is a widely used open-source thermophysical property library developed by researchers and engineers from academia and industry.

It provides accurate properties for refrigerants, water, air, and many other fluids, including density, enthalpy, entropy, viscosity, thermal conductivity, and saturation properties. CoolProp is used in education, research, and engineering applications worldwide.

For more information, see the article Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp .