Table of specific heat capacities

See also: List of thermal conductivities

Note that especially high values, as for paraffin, water and ammonia, result from calculating specific heats in terms of

moles of molecules. If specific heat is expressed per mole of atoms for these substances, few constant-volume

values exceed the theoretical Dulong-Petit limit of 25 J/(mol·K) = 3 R per mole of atoms.

Table of specific heat capacities at 25 °C (298 K) unless otherwise noted

Substance Phase cp

J·g−1·K−1

Cp,m

J·mol−1·K−1

Cv,m

J·mol−1·K−1

Volumetricheat capacity

J·cm−3·K−1

Air (Sea level, dry, 0 °C (273.15 K)) gas 1.0035 29.07 20.7643 0.001297

Air (typical room conditionsA) gas 1.012 29.19 20.85 0.00121

Aluminum solid 0.897 24.2 2.422

Ammonia liquid 4.700 80.08 3.263

Animal (incl. human) tissue [19] mixed 3.5 — 3.7*

Antimony solid 0.207 25.2 1.386

Argon gas 0.5203 20.7862 12.4717

Arsenic solid 0.328 24.6 1.878

Beryllium solid 1.82 16.4 3.367

Bismuth [20] solid 0.123 25.7 1.20

Cadmium solid 0.231 — —

Table of specific heat capacities at 25 °C (298 K) unless otherwise noted

Substance Phase cp

J·g−1·K−1

Cp,m

J·mol−1·K−1

Cv,m

J·mol−1·K−1

Volumetricheat capacity

J·cm−3·K−1

Carbon dioxide CO2[16] gas 0.839* 36.94 28.46

Chromium solid 0.449 — —

Copper solid 0.385 24.47 3.45

Diamond solid 0.5091 6.115 1.782

Ethanol liquid 2.44 112 1.925

Gasoline liquid 2.22 228 1.64

Glass [20] solid 0.84

Gold solid 0.129 25.42 2.492

Granite [20] solid 0.790 2.17

Graphite solid 0.710 8.53 1.534

Helium gas 5.1932 20.7862 12.4717

Hydrogen gas 14.30 28.82

Hydrogen sulfide H2S[16] gas 1.015* 34.60

Table of specific heat capacities at 25 °C (298 K) unless otherwise noted

Substance Phase cp

J·g−1·K−1

Cp,m

J·mol−1·K−1

Cv,m

J·mol−1·K−1

Volumetricheat capacity

J·cm−3·K−1

Iron solid 0.45025.1[citation

needed] 3.537

Lead solid 0.129 26.4 1.44

Lithium solid 3.58 24.8 1.912

Lithium at 181 °C[21] liquid 4.379 30.33 2.242

Magnesium solid 1.02 24.9 1.773

Mercury liquid 0.1395 27.98 1.888

Methane at 2 °C gas 2.191

Methanol liquid 2.597 — —

Nitrogen gas 1.040 29.12 20.8

Neon gas 1.0301 20.7862 12.4717

Oxygen gas 0.918 29.38

Paraffin wax solid 2.5 900 2.325

Polyethylene (rotomolding grade)

[22] solid 2.3027

Table of specific heat capacities at 25 °C (298 K) unless otherwise noted

Substance Phase cp

J·g−1·K−1

Cp,m

J·mol−1·K−1

Cv,m

J·mol−1·K−1

Volumetricheat capacity

J·cm−3·K−1

Polyethylene (rotomolding grade)

[22] liquid 2.9308

Silica (fused) solid 0.703 42.2 1.547

Silver [20] solid 0.233 24.9 2.44

Sodium solid 1.230 — —

Tin solid 0.227 — —

Titanium solid 0.523 — —

Tungsten [20] solid 0.134 24.8 2.58

Uranium solid 0.116 27.7 2.216

Water at 100 °C (steam) gas 2.080 37.47 28.03

Water at 25 °C liquid 4.1813 75.327 74.53 4.1796

Water at 100 °C liquid 4.1813 75.327 74.53 4.2160

Water at −10 °C (ice)[20] solid 2.11 38.09 1.938

Zinc [20] solid 0.387 25.2 2.76

Table of specific heat capacities at 25 °C (298 K) unless otherwise noted

Substance Phase cp

J·g−1·K−1

Cp,m

J·mol−1·K−1

Cv,m

J·mol−1·K−1

Volumetricheat capacity

J·cm−3·K−1

Substance Phase Cp

J/(g·K)

Cp,m

J/(mol·K)

Cv,m

J/(mol·K)

Volumetricheat capacity

J/(cm3·K)

A Assuming an altitude of 194 metres above mean sea level (the world–wide median altitude of human habitation), an indoor temperature of

23 °C, a dewpoint of 9 °C (40.85% relative humidity), and 760 mm–Hg sea level–corrected barometric pressure (molar water vapor content =

1.16%).

*Derived data by calculation. This is for water-rich tissues such as brain. The whole-body average figure for mammals is approximately 2.9

J/(cm3·K) [23]

[edit]Specific heat capacity of building materials

See also: Thermal mass

(Usually of interest to builders and solar designers)

Specific heat capacity of building materials

Substance Phasecp

J/(g·K)

Asphalt solid 0.920

Brick solid 0.840

Concrete solid 0.880

Glass, silica solid 0.840

Glass, crown solid 0.670

Glass, flint solid 0.503

Specific heat capacity of building materials

Substance Phasecp

J/(g·K)

Glass, pyrex solid 0.753

Granite solid 0.790

Gypsum solid 1.090

Marble, mica solid 0.880

Sand solid 0.835

Soil solid 0.800

Wood solid 1.7 (1.2 to 2.3)

Substance Phasecp

J/(g·K)

[edit]See also

http://en.wikipedia.org/wiki/Heat_capacity

Approximate specific heat capacities are given in this table:

Heat Capacity

While specific heat capacity refers to the material from which an object is made, e.g. aluminium, heat capacity refers to a particular object (the whole bulk of matter in an object, e.g. a calorimeter). In other words, specific heat capacity is a characteristic of a substance, whereas heat capacity relates to a particular object.

Therefore the heat capacity of an object depends on both its mass and the nature of the substance or substances from which it is made.

The symbol used is C and the units are joules per kelvin (J K –1). The heat capacity of an object is defined as the heat energy needed to increase the entire object’s temperature by 1 K.

http://www.seai.ie/Schools/Secondary_Schools/Subjects/Physics/Unit_5_-_Heat_Quantity/Heat_Capacity/

In Example 2.15.2, the water receives exactly the same amount of heat as the steam imparts (it is assumed there are no heat losses), but does so at a lower temperature than the steam; so, as entropy is given by enthalpy/temperature, dividing the same quantity of heat by a lower temperature means a greater gain in entropy by the water than is lost by the steam. There is therefore an overall gain in the system entropy, and an overall spreading out of energy.

Table 2.15.1

Relative densities/specific heat capacitiesof various solids

Table 2.15.2

Relative densities/specific heat capacitiesof various liquids

Table 2.15.3

Specific heat capacities of gases and vapours

http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-engineering-principles-and-heat-transfer/entropy-a-basic-understanding.asp

Following chart / table is very important for above equation.

ExampleCalculate the heat capacity of a 20-wt% Na2CO3 solution at 150 °F

SolutionStep-1Look up the heat capacity of this solid from table. If it is not available, apply Kopp's Rule, which says

Cp(Na2CO3) = 2 x Cp(Na) + 1 x Cp(C) + 3 x Cp(O)

From Table, we read the values at 150 °F (339 K). Notice that the heat capacity for oxygen is given as O2 (it's natural form). This value must be divided by two to get the heat capacity for one atom of oxygen.

So,Cp(Na) = 28.5612 KJ/Mole/KCp(C) = 11.6364 KJ/Mole/KCp(O) = 14.0611 KJ/Mole/K

So by Kopp's Rule

Cp (Na2CO3) = 2 x 28.5612 + 11.6364 + 3 x 14.0611= 110.9421 KJ/Mole/K

Step-2Now since our Dimoplon equation uses only weight basis, we need to divide this figure by molecular weight of compound. So,

Cp (Na2CO3) = 110.9421 / 105.9 = 1.0476 KJ/Kg/K

Now if you convert to Kcal then it becomes = 1.0476 x 0.23886 = 0.25 Kcal/Kg/K

Step-3Now note down the heat capacity of water at 150 F which is 0.9975 Kcal/Kg/K.

Step4Now finally apply Dimoplon rule as,W1 = 0.2 (20%)W2 = 0.8 (80%)Cpw = 0.9975Cps = 0.25

Hence,Cps = 0.2 x 0.25 + 0.8 x 0.9975Cps = 0.848 Kcal/Kg / K

ResultThe literature data for this system is reported as 0.850, SO there is a variation of only 0.2%. Thus Dimoplon rule gives a very good estimate of specific heat of solutions with dissolved solids.

The equations are useful for slurry systems where impacts are significant.Also it can be used for identification of specific heats of solids, where solid handling systems are involved with heat transfer.

http://profmaster.blogspot.com/2009/02/heat-capacity-with-dissolved-solids.html

Latin American applied researchversión ISSN 0327-0793

Lat. Am. appl. res. v.34 n.4 Bahía Blanca oct./dic. 2004

 

A new correlation for the specific heat of metals, metal oxides and metal fluorides as a function of temperature

S. I. Abu-Eishah1, Y. Haddad, A. Solieman, and A. Bajbouj2 1 Department of Chemical & Petroleum Engineering, UAEU, Al-Ain, UAE, siam20022001@yahoo.com 2 Chemical Engineering Department, Jordan University of Science & Technology, Irbid 22110, Jordan

Abstract  The objective of this work is to find a suitable correlation that best fits the specific heat of metals, metal oxides and metal fluorides as a function of temperature. It was found that a multilinear regression model of the form CP = aTbecTed/T has the lowest deviation from experimental data compared to other correlations including a 4th to 6th-order polynomial regression model. The coefficient of determination, R2, was very close to unity in most cases and the average of the absolute relative errors, AARE, was less than 5% for the specific heat of most of the systems studied. The overall AARE was about 1.8% for metals and 3% for metal oxides and metal fluorides, which is within the experimental error.

Key Words  Correlations. Metals. Metal Fluorides. Metal Oxides. Specific Heat.

I. Introduction

Materials are diverse in our life and have many uses. Many applications of metals, ceramics, fluxing materials and composites are based upon their unique thermophysical properties. Specific heat, thermal conductivity and thermal expansion are the properties that are often critical in the practical utilization of solids as materials of construction (Abu-Eishah, 2001a). These properties

depend upon the state, chemical composition, and physical structure of that material. They also depend on temperature and to a lesser extent on pressure, to which the material is subjected. In the design of rocket-engine thrust chambers, for example, considerable attention must be given to the effect of temperature on the thermophysical properties of its structure. The primary concern of engineers is to match the material properties to service requirements of the component, knowing the conditions of load and environment under which the component must operate. Engineers must then select an appropriate material, using tabulated test data, as the primary guide (Abu-Eishah, 2001b). Specific heat is the property that is indicative of materials ability to absorb heat from external surroundings. The specific heat of a material is largely determined by the effect of temperature on the vibration and rotational energies of the atoms within the material, the change in energy level of electrons in the structure of the material, and changes in atomic positions during formation of lattice defects (vacancies and interstitials), order-disorder transitions, magnetic orientation or polymorphic transformations (Richerson, 1992). In a previous work, Abu-Eishah (2001a) proposed a multilinear correlation to fit the thermal conductivity of metals as a function of temperature and found it among the best. In this study it is intended to check the suitability of such a multilinear correlation to fit the specific heat of metals, metal oxides and metal fluorides as a function of temperature.

II. Proposed Fitting Equations

The theories of the specific heat of metallic and non-metallic solids are covered in detail by Touloukian and Ho (1972a,b). The theoretical equation that represents the specific heat, in general, is given in Touloukian and Ho (1972a) as

CP = aT + bT 3 + c/T 2 (1)

The terms on the right-hand side of Eq. (1) belong to the electronic, lattice combination, and nuclear combination parts of the specific heat. Up to the knowledge of the authors, Eq. (1) was not used as is to fit the specific heat experimental data. Perry and Green (1997) give CP for pure compounds (metallic and non-metallic solids) as a linear equation of the form (CP = a + bT) for some compounds and by a nonlinear equation of the form (CP = a + bT + c/T 2) for others. The temperature range (starting at 273 K), the values of the coefficients a, b and c, and the uncertainty (%) of these correlations are also given in Perry and Green (1997) and summarized in Appendix. In this work, a wider and more comprehensive temperature ranges were covered compared to those used in Perry and Green (1997). The multilinear fitting equation proposed in this study has the form

CP = aTb ecT ed/T (2)

If the exponential terms in Eq. (2) are expanded by a Taylor's series, then we get

CP = aT b[A + BT + CT 2 + ... + D/T + E/T 2 + ...] (3)

which can be rewritten as

CP = A'T b + B'T b+1 + C'T b+2 + ... + D'/T b-1 + E'/T b-2 + ... (4)

where, A' = aA, B' = aB, etc. By comparing Eqs. (1) and (4), all terms in Eq. (1) are almost there in Eq. (4), but Eq. (4) has extra merits; it is more than just a polynomial, a power or an exponential function, it is a combination of all of these functions. It can have positive and negative exponents, with integer and non-integer values. Also, while Eq. (1) may predict negative specific heat at low temperatures, the parameter a in Eq. (2) is always nonnegative, which is needed for presenting always positive thermophysical data such as specific heat. Taking the logarithm of both sides of Eq. (2) gives

ln CP = ln a + b lnT + cT + d/T (5)

T in Kelvin and a, b, c and d are fitting constants. That is, Eq. (5) can be rewritten as

Y = a1 X1 + a2 X2+ a3 X3 + a4 X4 (6)

where a1 = ln a, a2 = b, a3 = c, a4 = d, and Y = ln CP, X1 = 1.0, X2 = ln T, X3 = T, and X4 = 1/T. That is, all terms in Eq. (6) are linear in Xi, i = 1, 2, 3, and 4; from which the multilinear name of the proposed model is derived. In addition to the multilinear regression, and for comparison purposes, an nth-order polynomial model of the form

CP = B0 + B1T + B2T 2+ B3T 3 + ... + BnT n (7)

is used in this study. Here B0, B1, B2 ... Bn are the polynomial fitting parameters. Although the polynomial regression method is well known and easy to implement on digital computers, its main disadvantages are more fitting parameters are needed to get higher accuracy, and it might give impractical (or unrealistic negative) values for the predicted property. Polynomials are based on power laws and diverge greatly at or near the end points of the data region. They are thus poor candidates for fitting "smooth" curves. In addition, polynomials force a certain number of inflection points that may not be in the "real" behavior of the physical property. No body can claim any physical significance of the parameters of the proposed model, at least for the time being, but this model, which is a combination of power and exponential series, is characterized by (a) smaller number of fitting parameters and (b) a more realistic representation of the experimental data (no negative values, for example). The main disadvantage of this method is that it does not properly fit sharp changes in the physical properties.

III. Results and Discussion

The experimental data for the specific heat of metals, metal oxides and metal fluorides were taken from Touloukian and Ho (1972a,b). Information about the purity, composition, and specifications concerning the samples used originally for experimental analysis as well as the reported error (last column of Appendix) are available in Touloukian and Ho (1972a). Throughout the analysis of results, the following basic definitions have been used:

Absolute Error, AE = |CPexp - CPcal|

Absolute Relative Error, ARE = |CPexp - CPcal|/CPexp

Average of Absolute Errors, 

AAE = (Absolute Errors)/M

Average of Absolute Relative Errors, 

AARE = (Absolute Relative Errors)/M

M is the number of data points in a given set of data. The coefficient of determination, R2, is defined in terms of the symbols used in Eq. (6) as

 (8)

and the standard error of estimate, SSE, is defined as

 (9)

where  , and i = 1, 2, ..., M and j = 1, 2, ... 4.

The experimental data used for metals, metal oxides and metal fluorides were taken from Touloukian and Ho (1972a,b) on the basis of very similar purity and composition of the chosen samples (curves). It should be mentioned first that, up to the knowledge of the authors, there is no single equation that fits all the temperature range of the specific heat of the studied systems. Equation (1) is just a proposed theoretical formula, but not used to fit the experimental specific heat data of the studied systems. For all the metal samples used, any impurity in the sample is less than 0.2% each, and the total impurity in any sample is less than

0.5% (Touloukian and Ho, 1972a,b). Table 1 shows the calculated fitting parameters for the specific heat of metals, the coefficient of determination,R2, and the average of the absolute relative error, AARE. R2 values are very close to unity, the values of AARE are less than 5%, and the overall AARE is about 1.8%, which is within the experimental error. The standard error of

estimate, SEE, defined by Eq. (9) is shown on the last column of Table 1. The values of SEE are generally low, and vary in accordance with the AARE values. A comparison between the calculated and experimental data for the specific heat of metals is

shown in Figs. 1 to 3, where the match is thought to be sufficient.

 Fig. 1: 1st set of calculated heat capacity of metals as a function of temperature using proposed multilinear regression

model vs. experimental data (Touloukian and Ho, 1972a).

 Fig. 2: 2nd set of calculated heat capacity of metals as a function of temperature using proposed multilinear

regression model vs. experimental data (Touloukian and Ho, 1972a).

Fig. 3: 3rd set of calculated heat capacity of metals as a function of temperature using proposed multilinear regression model vs. experimental data (Touloukian and Ho, 1972a).

In order to get the best fit, the data points for some metals (see Table 1) were divided here into two sets; low temperature range and high temperature range. On the other hand, when the full range of temperature for those metals were considered, the AARE

jumps to above 10% and reaches 31%, see Table 2. In order to compare the proposed model in Eq. (3) or (5) with that given in Perry's Handbook (1997), one needs to consider the temperature range used for both equations. The temperature range used for Perry's Handbook equation starts from 273 K and above, while that for Eq. (5) may start at as low as a few degrees K. Thus the comparison might not be valid for many of the

studied systems. Anyway, the proposed model in Eq. (5) fits the specific heat of aluminum and molybdenum, for example, better

than Perry's Handbook equation for the temperature range shown in Fig. 4. It should be mentioned, as shown in the last column of Appendix, that the reported error for the studied metals is ranging from 0.1 to 5%, and some samples have no reported error (Touloukian and Ho, 1972a). To make things shorter, no summary tables are included here for the polynomial regression results of the specific heat of the studied metals.

Fig. 4: Calculated specific heat vs. temperature for Al and Mo using (CP = a + bT + c/T 2) proposed in Perry and Green (1997) and Eq. (5) proposed in this work.

Table 3 shows a comparison between the fittings of a 4th-order polynomial model and the multilinear regression model for the specific heat of metal oxides and metal fluorides. The reported error for these metal oxides and metal fluorides ranges from 0.1 to 5%, except for uranium oxides (U3O8) where it reaches 15% (Touloukian and Ho, 1972b), and some samples have no reported

error. Again as shown in Table 3, although the polynomial model has R2 > 0.98, the corresponding AARE for the specific heat of some metal oxides is so high (190% for Li2O, 102% for MgO, 120% for SiO2 quartz glass, and 77% for SiO2 quartz crystal). This is because of the prediction of negative values for the specific heat of those metal oxides. For other metal oxides, R2 may be as low as 0.23 (for U3O8) while AARE = 4.6%, R2 = 0.86 (for Cr2O3) and AARE = 7.7%, or R2 = 0.9985 (for SiO2 cristobalite) and AARE = 12.4%. 

The corresponding values of R2 and AARE for the multilinear method are much better (see Table 3) with no non-realistic prediction of the specific heat. The maximum AARE is less than 5% and reaches only 14.5% for Li2O, 16.7% for MgO, and 8.8% for SiO2 quartz glass. Again for U3O8, although R2 is low (0.146) due to the uncertainty of the original data (15%) in Touloukian and Ho (1972b), the value of AARE is very similar to the polynomial model prediction and equals only 4.5%. 

For the studied metal fluorides, Table 3 shows that the polynomial model predictions are very close to those of the multilinear model except for KF where AARE reaches 25% (because of the negative values prediction) while the corresponding value for KF using the multilinear model is only about 4.1%. Otherwise, the maximum error in the 4th-order polynomial model predictions

reaches 7.2% for CaF2. In brief, the multilinear model has an overall AARE of only 3% for all the systems shown in Table 3, which is again within the reported experimental error. 

Lastly, the calculated fitting parameters for the specific heat as a function of temperature are shown in Tables 4 and 5 for metal oxides and metal fluorides using the polynomial and multilinear regression methods, respectively.

IV. Conclusions

In this work, a multilinear regression model of the form CP = aTb ecT ed/T was used to fit the specific heat of several metals, metal oxides, and metal fluorides as a function of temperature. The coefficient of determination, R2, was very close to unity for most of the systems studied. The average of the absolute relative errors, AARE, did not exceed 5% for the systems studied, except for Li2O and MgO where it reaches 14.5% and 16.7%, respectively. The overall AARE was about 1.8% for metals, and 3.0% for metal oxides and metal fluorides, which is within the experimental error. On the other hand, the polynomial fitting correlation, gave very close, and sometimes better, predictions for the specific heat of metals, metal oxides, and metal fluorides where the coefficient of determination, R2, was very close to unity in most cases and the average of the absolute relative errors, AARE, was less than 7.7% except for thorium (8.5%), and Li2O (190%), MgO (102%), SiO2 quartz glass (120%), SiO2 quartz crystal (77%), and potassium fluoride (25%). The polynomial method failed here because of the unrealistic negative values predicted for the specific heat of those systems.

Nomenclature

AARE Average of absolute relative errors a1, a2, a3, a4 Constants in Eq. (6) a, b, c, d Multilinear equation coefficients, Eqs. (1), (2) A, B ... E Constants in Eq. (3) B0, B1 ... Bn Polynomial coefficients, Eq. (7) CP Specific heat at constant pressure, kJ.kg-1.K-1 M Number of data points in a given set of data R2 Coefficient of determination, Eq. (8) SEE Standard error of estimate, Eq. (9) T Temperature, K

Subscripts

cal Calculated exp Experimental

Table 1: Multilinear Regression Parameters and R2 and AARE for the Specific Heat of Metals (cal.g-1.K-1 = 4.186 kJ.kg-1.K-1). Experimental Data from Touloukian and Ho (1972a)

Table 2: Multilinear Regression Parameters and R2, SEE, and AARE for the Specific Heat of Some Metals with Full- Range Data (cal.g-1.K-1 = 4.186 kJ.kg-1.K-1).

Table 3: R2 and AARE for the Specific Heat of Metal Oxides and Metal Fluorides for Polynomial and Multi-linear Fittings. Experimental Data from Touloukian and Ho (1972b)

Table 4: Multilinear Regression Parameters for the Specific Heat of Metal Oxides and Metal Fluorides (cal.mol-

1.K-1 = 4.186 kJ.kg-1.K-1). Experimental Data from Touloukian and Ho (1972b)

Table 5: 4th-order Polynomial Parameters for the Specific Heat of Metal Oxides (cal.mol-1.K-1). Experimental Data from Touloukian and Ho (1972b)

Appendix: Heat Capacity Coefficients for Metals, Metal Oxides and Metal Fluorides for CP = a + bT +c/T2 (cal.mol-1.K-1) and Uncertainty (Perry and Green, 1997), and Reported Error as given by Touloukian and Ho (1972a,b).

References 1. Abu-Eishah, S.I., "Correlations for the thermal conductivity of metals as a function of temperature", Int. J. Thermophys., 22:1855 (2001a). 2. Abu-Eishah, S.I., "Modeling of thermophysical properties of pure metals as a function of temperature", Int. Conf. on Advances in Production and Processing of Aluminum, APPA 2001, 12-15 Feb., Bahrain, p. 15-1-1 to 15-1-14 ( 2001b). 3. Perry, R.H. and D.W. Green (Editors), Perry's Chemical Engineer's Handbook, 7th ed., McGraw-Hill, New York (1997). 4. Richerson, D.W., Modern Ceramic Engineering: Properties, Processing, and Use in Design, 2nd ed. (Marcel Dekker, New York (1992). 5. Touloukian, Y.S. and C.Y. Ho (Editors), Thermophysical Properties of Matter, Specific Heat-Metallic Elements and Alloys, Vol. 4, Plenum Press, N.Y. (1972a). 6. Touloukian, Y.S. and C.Y. Ho (Editors), Thermophysical Properties of Matter, Specific Heat-Nonmetallic Solids, Vol. 5, Plenum Press, N.Y. (1972b).

http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0327-07932004000400009

HEAT STORAGE

All materials can store heat to some degree.  The ability of a material to do so is called its specific heat – the amount of heat,

measured in BTU’s for a given mass, a material can hold when its temperature is raised one degree Fahrenheit.  As an indicator of

a material's value as a heat storage medium in solar heating of spaces, the specific heat of a material is not very useful.  The

usefulness of a material in such an application is determined by its heat capacity, a measurement of the specific heat of a material

multiplied by its density. The higher the heat capacity, the more effective the material is for heating and cooling.

Finally, a good storage medium material must absorb heat when it is available, and give I t up when it is needed, and it must be a relatively good heat conductor. In Table 1 the comparative specific heat and heat capacity measurements for a variety of materials is given, and it shows there is no perfect storage medium in terms of volume, storage capacity, and conductivity.

Table 1. Specific heat and heat capacity of various surfaces.

http://www.azsolarcenter.org/tech-science/solar-for-consumers/passive-solar-energy/passive-solar-design-manual-consumer.html

Heat and WorkTemperature and HeatIn a qualitative sense, the temperature of an object determines the sensation of warmth or coldness felt from contact with it. A more rigourous definition is that temperature is the average kinetic energy of the atoms and molecules in a substance. When a high temperature object is placed in contact with a

low temperature object, then energy will flow from the high temperature object to the lower temperature object, and they will approach an equilibrium temperature. Note that temperature is not directly proportional to internal energy because temperature measures only the kinetic energy part of the internal energy, so two objects with the same temperature do not in general have the same internal energy]. The internal energy may be increased by transferring energy to the object from a higher temperature (hotter) object, a process called heating.

There are three main temperature scales used in the world - Celsius, Fahrenheit, and Kelvin. These are compared in the following table.Temperature Scale comparisons

  °C K °F

Water boils 100 373 212

Water freezes

0 273 32

Absolute zero

-273 0 -459

The relationship between temperature and heat is described by the concept of specific heat, which is the amount of heat required to change a unit mass of a substance by one degree in temperature. An equivalent statement is that specific heat is the amount of heat a material can hold when its temperature is raised one degree C.

Q = m · c · ΔTwhere m = mass in kilograms (kg), c = specific heat heat in joules per kilogram-degree centigrade

(J/kg/°C) and T = degrees Centrigrade.The specific heat of water is 1 calorie/gram/°C = 4.186 joule/gram/°C which is higher than any other common substance. This property of water allows it to absorb or release large amounts of heat without changing its temperature dramatically. As a result, water plays a very important role in temperature regulation since it allows the large bodies of water on the earth's surface to moderate our climate so that temperatures do not get too hot or too cold.

This is a very important feature in our lives. Some other important definitions related to energy, temperature, and heat are:

Heat Capacity - of a substance is the ratio of the amount of heat energy absorbed by that substance to its corresponding temperature rise.

Sensible Heat - is heat that can be measured by a thermometer, and thus sensed by humans. Several different scales of measurement exist for measuring sensible heat. The most common are: Celsius scale, Fahrenheit scale, and the Kelvin scale.

Latent Heat - is the energy required to change a substance to a higher state of

matter. This same energy is released from the substance when the change of state is reversed. The diagram below describes the various exchanges of heat involved with 1 gram of water.

Heat TransferHeat EnginesThe Second law of Thermodynamics 

Citation

http://www.eoearth.org/article/Energy

LIQUID CAUSTIC SODA – NEUTRALISATION

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Introduction

Definition: Neutralisation is a reaction in which the hydrogen ion (H

+

) of an acid and the hydroxyl ion

(OH

-

) of a base unite to form water, the other product being a salt.

Hydrochloric acid may be neutralised with sodium hydroxide solution (and vice versa) but only with

special precaution to avoid splashes or exposure to fumes.

The reaction is strongly exothermic. To avoid an excessive temperature increase, dilute concentrated

solutions before neutralisation!

Reaction: NaOH (l) + HCl (l) -> NaCl (l) + H2O (l)

NaOH = Liquid Caustic Soda

HCl = Hydrochloric Acid

NaCl = Sodium Chloride

H2O = Water

(l) = liquid

Please consult our safety data sheets

___________________________________________________________________________________

Thermodynamic definitions and formulas

The heat (q) released by the reaction is:

q = - n x ΔrH

With n = moles of NaCl formed and ΔrH heat of reaction as calculated by Hess’s Law

Hess’s Law: “The heat of reaction ΔrH can be obtained by subtracting the heat of formation of the

reactives from the heat of formation of the products.”

For exothermic reactions ΔrH is negative. ΔrH is quoted in units of kJ mol

-1

.

The appropriate ΔH values, assuming standard conditions at 298.15 K and 1 bar, are available from

“The NBS tables of chemical thermodynamic properties – Journal of Physical and Chemical Reference

Data Volume 11,1982 Supplement No. 2”, published by the American Chemical Society and the

American Institute of Physics for the National Bureau of Standards.

The heat (Q) absorbed by the solution results in a change of temperature.

Q = cp m ΔT

With cp = specific heat (J kg

-1

K

-1

), m is the mass (kg) and ΔT (K) is the change of temperature.

Conservation of energy

Q = q

cp m ΔT = - n x ΔrH

Note: We assume that the heat is not transferred to the environment (adiabatic conditions).

___________________________________________________________________________________

Calculation method of the temperature increase (Example)

What would the temperature increase ΔT be when 1 kg Liquid Caustic Soda 13% (130 g / kg) is

neutralised with the stoechiometric amount of Hydrochloric Acid 33% (330 g / kg)? LIQUID CAUSTIC SODA – NEUTRALISATION

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Calculation of q = n x ΔrH

Calculate the factors Moles H2O / Moles product

For the HCl solution: N(HCl

) = n H2O / n HCl

= {(1000 – 330) / 18.02} / {(330 / 36.45)} = 4.11

For the NaOH solution: N(NaOH) = n H2O / n NaOH = {(1000 – 130) / 18.02} / {(130 / 40.00)} = 14.85

For the NaCl solution: N(NaCl

) = N(NaOH) + N(HCl

) + 1 = 4.05 + 14.85 + 1 = 19.96

Use these factors to find the appropriate ΔH values in the NSB tables and interpolate if necessary:

ΔH(HCl

) = -153.266 kJ mol

-1

HCl

ΔH(NaOH) = -470.147 kJ mol

-1

NaOH

ΔH(NaCl

) = -408.420 kJ mol

-1

NaCl

ΔH(H2O) = -285.830 kJ mol

-1

H2O

Calculate the heat of reaction by using Hess’s law

ΔrH = ΔH(H2O) + ΔH(NaCl

) - ΔH(HCl

) - ΔH(NaOH) = -70.84 kJ mol

-1

The moles of NaCl formed are equal to the moles of NaOH to be neutralized.

n NaCl

= n NaOH = m / M = 130 /40 = 3.25 mol NaOH

With m = mass of NaOH (g) and M = molecular mass of NaOH (g mol-1)

Calculate the heat released

q = - n NaCl

x ΔrH = - 3.25 x -70.84 = 230.23 kJ

Calculation of the temperature increase ΔT

Calculate the required mass of HCl 33%

m(HCl 33%) = n HCl

x M /0.33 = 3.25 x 36.45 / 0.33 = 359 g HCl 33%

With n HCl

= moles of HCl (mol) and M molecular mass of HCl (g mol

-1

)

Note: n HCl = n NaOH

Calculate the total mass of formed NaCl in solution

m NaCl = m (NaOH 13%)

+ m (HCl 33%) = 1000 g + 359 g= 1359 g or 1.359 kg

Calculate the concentration of NaCl in the solution

C NaCl

= n NaCl

x M / m NaCl

= 3.25 x 58.45 / 1.359 = 140 g / kg

With M molecular mass of NaCl (g mol

-1

)

Interpolate the cp of the NaCl solution as per enclosed table.

The specific heat at constant pressure (cp) of NaCl solutions is given in enclosed table (at 40ºC):

Concentration of NaCl , g/kg cp, kJ kg

-1

K

-1

50 3.906

100 3.745

150 3.574

cp of the NaCl solution = 3.609 kJ kg

-1

K

-1

Note: Although the specific heat of NaCl solutions depends on the temperature, the correction due to

temperature effect on Cp would be of minor relevance and the temperature increase ΔT would not differ

significantly.

ΔT = q / (cp x m) = 230.23 kJ / (1.359 kg x 3.609 kJ kg

-1

K

-1

) = 46.9 K

The temperature increase of the solution after neutralisation would be 46.9 K or 46.9 °C. LIQUID CAUSTIC SODA – NEUTRALISATION

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The appropriate ΔH values, assuming standard conditions at 298.15 K and 1 bar, are available directly or through

interpolation in “The NBS tables of chemical thermodynamic properties – Journal of Physical and Chemical

Reference Data Volume 11,1982 Supplement No. 2”, published by the American Chemical Society and the American

Institute of Physics for the National Bureau of Standards.

Moles of H2O per mol HCl Heat of formation , kJ/mol HCl

1 -121.55

1.5 -132.67

2. -140.96

2.5 -145.48

3. -148.49

4. -152.917

4.5 -154.503

5. -155.774

6. -157.682

8. -160.005

10. -161.318

12. -162.180

15. -163.025

20. -163.845

25. -164.339

30. -164.670

40. -165.096

50. -165.356

moles of H2O per mole of NaOH Heat of formation , kJ/mol NaOH

2.5 -452.290

3. -456.278

4. -461.935

4.5 - 463.784

5. -465.185

6. -467.072

8. -468.905

10. -469.646

12. -469.972

15. -470.156

20. -470.198

25. -470.131

30. -470.060

40. -469.930

50. -469.834

moles of H2O per mole of NaCl Heat of formation , kJ/mol NaCl

9. -409.279

10. -409.233

12. -409.070

15. -408.806

20. -408.417

25. -408.137

30. -407.923

40. -407.626

50. -407.442

Heat of formation , kJ/mol H2O

1 mol H2O -285.830

__________________________________________________________________________________________________________

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any warranty, express or implied, or accept any liability in connection with this information or its use. This information is for use by

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Specific Heat and Heat Capacity

 

Specific heat is another physical property of matter. All matter has a tem-perature associated with it. The temperature of matter is a direct measure of the motion of the molecules: The greater the motion the higher the temperature:

Motion requires energy: The more energy matter has the higher tempera-ture it will also have. Typicall this energy is supplied by heat. Heat loss or gain by matter is equivalent energy loss or gain.

With the observation above understood we con now ask the following question: by how much will the temperature of an object increase or de-crease by the gain or loss of heat energy? The answer is given by the spe-cific heat (S) of the object. The specific heat of an object is defined in the following way: Take an object of mass m, put in x amount of heat and carefully note the temperature rise, then S is given by

In this definition mass is usually in either grams or kilograms and temperatture is either in kelvin or degres Celcius. Note that the specific heat is "per unit mass". Thus, the specific heat of a gallon of milk is equal to the specific heat of a quart of milk. A related quantity is called the heat capacity (C). of an object. The relation between S and C is C = (mass of obect) x (specific heat of object). A table of some common specific heats and heat capacities is given below:

Some common specific heats and heat capacities:

 Substance S

(J/g0C)

 C (J/0C)

for 100 g

 Air  1.01  101

 Aluminum  0.902  90.2

 Copper  0.385  38.5

 Gold  0.129  12.9

 Iron  0.450  45.0

 Mercury  0.140  14.0

 NaCl  0.864  86.4

 Ice  2..03  203

 Water  4.179  41.79

     

Consider the specific heat of copper , 0.385 J/g 0C. What this means is

that it takes 0.385 Joules of heat to raise 1 gram of copper 1 degree cel-cius. Thus, if we take 1 gram of copper at 25 0C and add 1 Joule of heat to it, we will find that the temperature of the copper will have risen to 26 0C. We can then ask: How much heat wil it take to raise by 1 0C 2g of copper?. Clearly the answer is 0.385 J for each gram or 2x0.385 J = 0.770 J. What about a pound of copper? A simple way of dealing with different masses of matter is to dtermine the heat capacity C as defined above. Note that C depends upon the size of the object as opposed to S that does not.

We are not in position to do some calculations with S and C.

Example 1: How much energy does it take to raise the temperature of 50 g of copper by 10 0C?

Example 2: If we add 30 J of heat to 10 g of aluminum, by how much will its temperature increase?

 

Thus, if the initial temperture of the aluminum was 20 0C then after the heat is added the temperature will be 28.3 0C.

http://www.iun.edu/~cpanhd/C101webnotes/matter-and-energy/specificheat.html