<Thermolphysical properties of matter>
Properties of solids and liquids

thermal conductivity	k_ 	[W/m-K or Btu/hr-ft-R]

density	rho_	[kg/m^3 or lbm/ft^3]

specific heat	c_	[kJ/kg-K or Btu/lbm-R]

viscosity (dynamic)	mu_	[N-s/m^2 or lbm/hr-ft]

volumetric thermal expansion coeff.	beta_	[1/K, 1/R] (note: beta=3*alpha)

modulus of elasticity (Young's mod.)	E_	[GPa, psi]

Poisson's ratio	nu_	[-, -]

linear thermal expansion coeff.	alpha_	[1/K, 1/R] (note: alpha=beta/3)

linear expansion	ΔL\L_293_	[-,-] (the change in length relative

to the length at 20C [ 68F])

Usage

Error and Warning Messages

Adding new substances

Adding new types of data

Substances at one temperature

Multiple temperature ranges for one substance

Ideal gas

Substances and allowable temperature range.

Metals

Nonmetallic Solids

Structural Building Materials

Insulating Materials and Systems

Industrial Insulation

Miscellaneous Materials

Saturated or Compressed Fluids

Liquid metals

References

Usage   Back to top

The thermal conductivity k_, density rho_, specific heat c_, viscosity mu_, volumetric thermal expansion coefficient beta_, elastic modulus E_, linear coefficient of thermal expansion alpha_ and Poisson's ratio nu_ of a variety of substances (solids, saturated or compressed liquids, and ideal gases) are available as functions of temperature using the EES user supplied library Solid-Liquid_Props.  Not all of these properties are available for all listed substances and other properties may be added.  As an example, the thermal conductivity of copper at a temperature of 500 (K, C, R or F depending upon the EES units setting) is obtained with the EES equation, k=k_('copper', 500).  The following EES example illustrates usage (with the temperature units set to K) using the substance mercury-liquid:

substance$='mercury-liquid'

T=350                      	"[K]"

k=k_(substance$, T)	"[W/m-K]"

rho=rho_('mercury-liquid' T)	"[kg/m^3]"

c=c_(substance$, 350)*Convert(kJ, J) "[J/kg-K] note conversion to J from kJ"

mu=mu_(substance$, T)	"[N-s/m^2]"

beta=beta_(substance$, T)	"[1/K]"

alpha=k/(rho*c) 	"[m^2/s]  thermal diffusivity"

nu=mu/rho	"[m^2/s]"

Pr=nu/alpha	"[ ]"

Note that the substance can be a string (e.g., substance$) or a case insensitive string constant (e.g., 'mercury-liquid').  The temperature can be a variable (e.g., T) or a number (e.g., 350).  Unlike the EES built-in functions, the format T=T or T=350 is not allowed.  If the EES units were set to SI and K in the above example the results would be:

ρ=13407	[kg/m^3]

c=137.7	[J/kg-K] "note J not kJ due to the use of the convert function"

k=9.18	[W/m-K]

μ=0.001309	[N-s/m^2]

β=0.000181	[1/K]

α=4.973E-06	[m^2/s]

ν=9.76E-08	[m^2/s]

Pr=0.01964	[ ]

In this EES example, alpha is the thermal diffusivity. The function alpha_  does not return the thermal diffusivity but returns the linear coefficient of thermal expansion with units of 1/K or 1/R.  The volumetric coefficient of thermal expansion, beta,  is commonly used in thermal problems whereas the linear coefficient of thermal expansion, alpha, is commonly used in mechanics problems.  The two coefficients are related by beta=3*alpha.

The density variation with temperature of most solids (metals and nonmetalic solids) was calculated from the density at a known temperature (usually 293K) and DELTAL\L_293, the change in length relative to the length at 293K (20C or 68F).  Thus, if the density is known at 300K to be 8933 kg/m^3 (copper) then the density at a  temperature of 800K is found from the value of DELTAL\L_293 at 800K from:

rho_300=8933  " [kg/m^3]"

DELTAL\L_293=0.00939

rho_T=rho_300/(1+DELTAL\L_293)^3

The elastic modulus, E and the shear modulus, G, are related through Poisson's ratio, ν, by E/G=2*(1+ν).  Note that ν here is Poisson's ratio and not the kinematic viscosity.

The EES units setting can be either SI or English and the temperature is assumed to be K, C, R or F, depending upon the EES units temperature setting.  The values returned are the appropriate SI or English units as shown at the top of this file.

The data are stored in lookup tables with the general form (shown for mercury-liquid):

T	rho	c	k	mu	beta

[K]	[kg/m^3]	[kJ/kg-K]	[W/m-K]	[N-s/m^2]	[1/K]

273	13595	0.140	8.18	0.001688	0.000181

300	13529	0.139	8.54	0.001523	0.000181

350	13407	0.138	9.18	0.001309	0.000181

400	13287	0.137	9.8	0.001171	0.000181

450	13167	0.136	10.4	0.001075	0.000181

500	13048	0.135	10.95	0.001007	0.000182

550	12929	0.135	11.45	0.000953	0.000184

600	12809	0.136	11.95	0.000911	0.000187

The units of the data in the lookup table must be in SI units as indicated at the top of this file.  The name of the above lookup table is Mercury.lkt so that substance is 'mercury'.  The values returned are obtained by linear interpolation.  Not all of the properties need to be supplied for each substance (of course for solids the viscosity has no meaning).  Other materials can be added - see adding new substances.  Other properties can be added - see adding new types of data.

If temperature dependent property data is known for two different temperature ranges, blanks can be used in the property column.  Suppose beta in the mercury-liquid table were known for the secondary temperature range from 350 K to 450K and all other properties are know for the primary temperatue range of 273 to 600K.  The table would then look like:

T	rho	c	k	mu	beta

[K]	[kg/m^3]	[kJ/kg-K]	[W/m-K]	[N-s/m^2]	[1/K]

273	13595	0.140	8.18	0.001688

300	13529	0.139	8.54	0.001523

350	13407	0.138	9.18	0.001309	0.000181

400	13287	0.137	9.8	0.001171	0.000181

450	13167	0.136	10.4	0.001075	0.000181

500	13048	0.135	10.95	0.001007

550	12929	0.135	11.45	0.000953

600	12809	0.136	11.95	0.000911

If beta is requested for a temperature outside the secondary range 350-450K, an error message will be issued and EES will stop.  Note that if a temperature of 650K (which is outside the primary range) were supplied to the rho_ function, a value of 12689 will be returned (linear extrapolation from 550 and 600 to 650) and a warning (not error) issued.

Error and Warning Messages   Back to top

Error messages will stop EES but Warning messages are displayed after the calculations are complete (even if the 'display warning messages' option in the menu Options\Preferences\Options is not checked).

If the library Solid-Liquid_Props is not loaded and if the function k_ (or any of the other functions: rho_, c_, mu_, beta_, etc.) is used, the error message 'The function k_ is not defined' will be displayed.  The Solid-Liquid_Props library will be automatically loaded if the folder 'Solid-Liquid_Props' is placed in the folder Userlib.

If the Solid/liquid Properties button is not accessable, check to make sure the file 'Solid-Liquid_Props.txt" is in the Solid-Liquid_Props folder in the Userlib folder.

If a property does not exist for a particular substance, e.g., beta_('soil', 300), an error message 'A column with the name beta was not found' will be displayed.  Such an error willl be generated with:  beta_soil=beta_('soil', 300)

If a material does not exist, e.g., 'mud', an error message 'A lookup table or file with the name Solid-Liquid_Props/mud' was not found' will be displayed.  Such an error willl be generated with:  rho_mud=rho_('mud', 300)

If the temperature specified for a material is outside of the primary allowable range, a warning message such as 'The temperature supplied to the solid density lookup table for mercury is 100 K. The allowable range is 273 to 600 K. ' will be displayed.   Such a warning willl be generated with:  rho_coldMercury=rho_('mercury-liquid', 100) when the temperature units are set to K or R.  Calculations will continue with the properties extrapolated (using the EES function Interpolate1) from the known temperatures.

If the temperatue specified for a material is outside a secondary allowable range, an error message will be issued and EES will stop.  See the example at the end of the Usage section.

Adding new substances   Back to top

New substances can be entered using the EES menu Tables\New Lookup Table.  Make a LookUp table with at least M columns and N rows where M is the number of properties N is the number of temperature points and must be at least 2.  The column headers must be the names found in the file Solid-Liquid_Props.TXT with T in the first column and without the underscore as the last character.  The order of the properties (other than T) is arbitrary and not all properties need to be supplied.  The units are optional but recommended.  The N temperatures must be in increasing order with any desired interval between adjacent entries.  If the lookup table is a part of the EES program, the data is available only in that program.  Save the table in the directory Userlib\Solid-Liquid_Props and the data is be available to other programs.

Adding new types of data   Back to top

New data types can be entered by modifying the file Solid-Liquid_Props.txt and the library function Solid-Liquid_Props.lib.  The text file contains the names of the property functions with an ending underscore and the property units in SI and English units.

beta_ [1/K]  [1/R]

c_ [kJ/kg-K]  [Btu/lbm-R]

k_ [W/m-K]  [Btu/hr-ft-R]

mu_ [N-s/m2]  [lbm/ft-hr]

rho_ [kg/m3]  [lbm/ft3]

E_ [GPa]  [psi]

alpha_ [1/K]  [1/R]

nu_ [] []

DELTAL\L_293 [] []

To add a new property, the name (ending with an underscore) and units must be added to the file Solid-Liquid_Props.TXT.  For example to add the yield strength function named yield_ the new entry in the file Solid-Liquid_Props.TXT would be:

yield_ [MPa] [ksi]

The lookup table for the property must then have a column named yield (no underscore).

It is also necessary to add the new function yield_ to the EES library Solid-Liquid_Props.  Load the library function Solid-Liquid_Props.lib and copy the statements for one of the existing properties (e.g., k_) and paste it at the bottom of the file.  Make the following changes (shown in blue and red).

Function k_ yield_(Substance$, T)

File$=substance$

LastRow=NLookupRows(File$)

T_max=Lookup(File$, LastRow,'T')

T_min=Lookup(File$, 1,'T')

Call CheckT_(T_min, T_max, T : T_K, T$, U$, High$, Low$)

If (T_K>T_max) or (T_K<T_min) then

a$=Concat$('The temperature supplied to the thermal conductivity yield strength lookup table for ', substance$)

b$=concat$(a$, ' is XXXF0' )

c$=Concat$(b$, U$)

d$=Concat$(c$, 'The allowable range is ')

e$= Concat$(d$, Low$)

f$=Concat$(e$, ' to ')

g$=Concat$(f$, High$)

h$=Concat$(g$, U$)

Call warning(h$, T)

EndIf

k_ yield_=interpolate1(File$,'T', 'kyield', T=T_K)*(UnitSystem('SI')+UnitSystem('Eng')*Convert(W/m-KMPa, Btu/hr-ft-R ksi))

end thermal conductivity yield strength

The Convert function converts the property units from SI to English.   When finished, save the modified file (it will be saved automatically as a library file).

Substances at one temperature   Back to top

In some instances the data is known for only one nominal temperature, e.g., 300K.  This is a common situation for building materials.  In this case two temperatures, slightly above and below the nominal value should be entered into the table, e.g., 299 and 301.  With this 300K nominal temperature and the 2K temperature range, using 27C, 540F or 80F, depending upon the units setting, will not generate a warning message.  However, if the temperature is outside this narrow range an error message will be generated as a reminder to the user that property data may not be what was expected.

T	rho	c	k

[K]	[kg/m^3]	[kJ/kg-K]	[W/m-K]

299	1920	0.835	0.72

301	1920	0.835	0.72

An alternate approach to the one temperature data set is to set the two temperatures to say 0 and 10000K.  In this case no warning messages will be issued for any temperature less than 10000K.

Multiple temperature ranges for one substance

Different property data (for one substance) may be available over two or more temperature ranges.  For example, the table below is for Carbon_steel.

T	rho	c	k	alpha	DELTAL\L_293

[K]	[kg/m^3]	[kJ/kg-K]	[W/m-K]	[μm/m]	[-]

300	7854	0.434	60.5	5.5	0.00006

400	7835	0.478	56.7	11.0	0.00086

600	7756	0.559	48.0	23.1	0.00425

700	7695	0.622	43,6	29.7	0.00689

800	0.685	39.2

1000	1.169	30.0

If the temperature is greater than 700K and less than or equal to 1000K only the properties c and k are available.

Ideal gas   Back to top

Most ideal gas data are available as EES built-in functions.  If additional data is available the data can be entered into EES lookup tables.  Properties that are functions only of temperature can be entered into these tables.  Consequently, density, entropy, etc., which are functions of temperature and pressure, cannot be placed in these tables.  Ideal gas properties that are functions of both T and p are easily calculated from ideal gas relationships.

Substances and allowable temperature range

Some substances have multiple temperature ranges.  Where they differ, the "Range of data" refers to the properties k, ρ, and c.

Metals   Back to top

Substance                                Range of data	Properties	Source

Aluminum	100K - 800K	k, ρ, c, α, ΔL/L, E, ν	0, 2, 3

Beryllium	100K - 1200K	k, ρ, c, α, ΔL/L	0, 3

Bismuth	100K - 400K 	k, ρ, c, α, ΔL/L	0, 3

Boron	100K - 1000K	k, ρ, c, α, ΔL/L	0, 3

Bronze	200K - 600K	k, ρ, c, α, ΔL/L	0, 3

Cadmium	100K - 400K	k, ρ, c, α, ΔL/L	0, 3

Chromium	100K - 2000K	k, ρ, c, α, ΔL/L	0, 3

Cobalt	100K - 1500K	k, ρ, c, α, ΔL/L	0, 3

Copper	100K - 1200K	k, ρ, c, α, ΔL/L	0, 3

Germanium	100K - 1200K	k, ρ, c, α, ΔL/L	0, 3

Gold	100K - 1200K	k, ρ, c, α, ΔL/L	0, 3

Iridium	100K - 1500K	k, ρ, c, α, ΔL/L	0, 3

Iron	100K - 1500K	k, ρ, c, α, ΔL/L	0, 3

  Iron_Armco	100K - 1500K	k, ρ, c, ΔL/L	0, 3

  Carbon_steel	300K - 1000K	k, ρ, c, α, ΔL/L	0, 3

  Carbon_steel_AISI1010	300K - 1000K	k, ρ, c, α, ΔL/L	0, 3

  Stainless_AISI302	300K - 1000K	k, ρ, c, α, ΔL/L, E, ν	0, 2, 3

  Stainless_AISI316	100K - 150K	k, ρ, c, α, ΔL/L	0, 3

  Stainless_AISI347	300K - 1000K	k, ρ, c, α, ΔL/L	0, 3

  Stainless_AISI304	300K - 1000K	k, ρ, c, α, ΔL/L	0, 3

Lead	100K - 600K	k, ρ, c, α, ΔL/L	0, 3

Magnesium	100K - 800K	k, ρ, c, α, ΔL/L	0, 3

Molybdenum	100K - 2500K	k, ρ, c, α, ΔL/L	0, 3

Nickel	100K - 1500K	k, ρ, c, α, ΔL/L	0, 3

Nichrome	300K - 800K	k, ρ, c, ΔL/L	0, 3

Inconel_X_750	100K - 1500K	k, ρ, c, α, ΔL/L	0, 3

Niobium	100K - 2000K	k, ρ, c, α, ΔL/L	0, 3

Palladium	100K - 1500K	k, ρ, c, α, ΔL/L	0, 3

Platinum	100K - 2000K	k, ρ, c, α, ΔL/L	0, 3

Rhenium	100K - 2000K	k, ρ, c, α, ΔL/L	0, 3

Rhodium	100K - 2000K	k, ρ, c, α, ΔL/L	0, 3

Silicon	100K - 1500K	k, ρ, c, α, ΔL/L	0, 3

Silver	100K - 1200K	k, ρ, c, α, ΔL/L	0, 3

Tantalum	100K - 2500K	k, ρ, c, α, ΔL/L	0, 3

Thorium	100K - 1200K	k, ρ, c, α, ΔL/L	0, 3

Tin	100K - 400K	k, ρ, c, α, ΔL/L	0, 3

Titanium	100K - 1500K	k, ρ, c, α, ΔL/L	0, 3

Tungsten	100K - 2500K	k, ρ, c, α, ΔL/L	0, 3

Uranium	100K - 1200K	k, ρ, c, α, ΔL/L	0, 3

Vanadium	100K - 2000K	k, ρ, c, α, ΔL/L	0, 3

Zinc	100K - 600K	k, ρ, c, α, ΔL/L	0, 3

Zirconium	100K - 2000K	k, ρ, c, α, ΔL/L	0, 3

Nonmetalic Solids   Back to top

Substance                                Range of data	Properties	Source

Al oxide-sapphire	300K - 1000K	k, ρ, c

Al oxide-polycryst	300K - 1000K	k, ρ, c, α, ΔL/L	0, 3

Beryllium oxide	300K - 2000K	k, ρ, c, α, ΔL/L	0, 3

Fused Silica	300K - 1200K	k, ρ, c, α, ΔL/L	0, 3

Sulfur	100K - 300K	k, ρ, c

Thorium dioxide	300K - 2000K	k, ρ, c, α, ΔL/L	0, 3

Titanium dioxide	300K - 1200K	k, ρ, c, α, ΔL/L	0, 3

Structural Building Materials   Back to top

Substance                                Range of data	Properties	Source

Plywood	300K 	k, ρ, c

Sheathing-regular density	300K  	k, ρ, c

Acoustic tile	300K  	k, ρ, c

Hardboard-siding	300K  	k, ρ, c

Hardboard-high density	300K  	k, ρ, c

Particle board-low density	300K  	k, ρ, c

Particle board-high density	300K  	k, ρ, c

Hardwoods-oak-maple	300K  	k, ρ, c

Softwoods-fir-pine	300K  	k, ρ, c

Cement mortar	300K  	k, ρ, c

Brick-common	300K 	k, ρ, c

Gypsum plaster&sand	300K 	k, ρ, c

Insulating Materials and Systems   Back to top

Substance                                Range of data	Properties	Source

Glass fiber batt rho=16	300K	k, ρ

Glass fiber batt rho=28	300K	k, ρ

Glass fiber batt rho=40	300K	k, ρ

Glass fiber duct liner	300K	k, ρ, c

Polystyrene R12 expanded	300K	k, ρ, c

Polystyrene molded beads	300K	k, ρ, c

Industrial Insulation   Back to top

Substance                                Range of data	Properties	Source

Blanket-glass fiber rho=12	240K - 365K	k, ρ

Blanket-glass fiber rho=16	240K - 365K	k, ρ

Blanket-glass fiber rho=24	240K - 365K	k, ρ

Blanket-glass fiber rho=32	240K - 365K	k, ρ

Blanket-glass fiber rho=48	240K - 365K	k, ρ

Blanket-Al-silica rho=48	530K - 750K	k, ρ

Blanket-Al-silica rho=64	530K - 750K	k, ρ

Blanket-Al-silica rho=96	530K - 750K	k, ρ

Blanket-Al-silica rho=128	530K - 750K	k, ρ

Pipe ins-Asbestos 4ply	300K - 365K	k, ρ

Pipe ins-Asbestos 6ply	300K - 365K	k, ρ

Pipe ins-Asbestos 8ply	300K - 365K	k, ρ

Pipe ins-magnesia 85%	310K - 420K	k, ρ

Pipe ins-calcium silicate	310K - 750K	k, ρ

Pipe ins-cellular glass	230K - 420K	k, ρ

Pipe ins-diatomaceous	530K - 750K	k, ρ

Pipe ins-silica	530K - 750K	k, ρ

Pipe ins-polystyrene extru56	200K - 310K	k, ρ

Pipe ins-polystyrene extru35	200K - 310K	k, ρ

Pipe ins-polystyrene beads	200K - 300K	k, ρ

loose fill-wood	285K - 310K	k, ρ

loose fill-perlite	200K - 310K	k, ρ

loose fill-vermiculite 122	230K - 310K	k, ρ

loose fill-vermiculite 80	230K - 310K	k, ρ

Miscellaneous Materials   Back to top

Substance                                Range of data	Properties	Source

Asphalt	300K	k, ρ, c

Bakelite	300K	k, ρ, c

Clay	300K	k, ρ, c

Coal-anthracite	300K	k, ρ, c

Concrete & stone mix	300K	k, ρ, c

Cotton	300K	k, ρ, c

Glass-soda lime	300K	k, ρ, c

Glass-Pyrex	300K	k, ρ, c

Ice	253K-273K	k, ρ, c

Paper	300K	k, ρ, c

Parafin	300K	k, ρ, c

Rock-granite	300K	k, ρ, c, E	0, 2

Rock-limestone	300K	k, ρ, c

Rock-marble	300K	k, ρ, c

Rock-quartzite	300K	k, ρ, c

Rock-sandstone	300K	k, ρ, c

Rubber-vulcanized soft	300K	k, ρ, c

Rubber-vulcanized hard	300K	k, ρ

Sand	300K	k, ρ, c

Soil	300K	k, ρ, c

Snow rho=110	273K	k, ρ

Snow rho=500	273K	k, ρ

Teflon	300K - 400K	k, ρ

Wood-cross balsa	300K	k, ρ

Wood-cross cypress	300K	k, ρ

Wood-cross fir	300K	k, ρ

Wood-cross oak	300K	k, ρ

Wood-cross yellow pine	300K	k, ρ

Wood-cross white pine	300K	k, ρ

Wood-radial oak	300K	k, ρ

Wood-radial fir	300K	k, ρ

Saturated or Compressed Fluids   Back to top

Substance                                Range of data	Properties	Source

Glycerin	273K - 320K 	k, ρ, c, μ, β

Engine oil-unused	273K - 430K	k, ρ, c, μ, β

Liquid metals - saturated   Back to top

Substance                                Range of data	Properties	Source

Bismuth-liquid	589K - 1033K	k, ρ, c, μ

Lead-liquid	644K - 977K	k, ρ, c, μ

Mercury-liquid	273K - 600K	k, ρ, c, μ, β

Potassium-liquid	422K - 977K	k, ρ, c, μ

Sodium-liquid	400K - 2500K	k, ρ, c, μ, β	1

NaK(45/55)-liquid	366K - 977K	k, ρ, c, μ

NaK(22/78)-liquid	366K - 1033K	k, ρ, c, μ

References   Back to top

If no source is indicated then it is from reference 0.  When properties are from more than one source, both are listed.  If a material has crystalline structure, the data are presented for the polycrystalline form.

0. Introduction to Heat Transfer, 3rd ed., Incropera and DeWitt, J. Wiley and Sons, 1996

1. Thermo Physical Properties of Sodium, J.K. Fink & L. Liebowitz, ANL-CEN-RSD-79-1, 1979

2. Advanced Mechanics of Materials, 2nd ed., R. .D. Cook and W. C. Young, Prentice Hall, 1999

3. Thermophysical Properties of Matter, Vol 1 through Vol 13., Touloukian, Y.S. and C.Y. Ho, Eds.,  Plenum Press, New York, 1972