Why Is Specific Heat Important

Mathematical modeling of heat transfer in biological tissues (bioheat transfer)

Dieter Haemmerich , in Principles and Technologies for Electromagnetic Energy Based Therapies, 2022

1.3.1 Specific heat capacity

The specific oestrus chapters c [J/(kg K)] of tissue describes how much energy is required to change the temperature of 1   kg of tissue by 1   K (=one°C). For example, the lower specific heat capacity of fat compared to other soft tissue indicates, that fat requires less energy to obtain a sure temperature increase. If nosotros multiply specific rut capacity past mass density (ρ·c [J/(one thousand³ 1000)]), nosotros obtain the energy required to enhance the temperature of i   1000³ of tissue past 1   1000 (=ane°C)—that is, a quantity equivalent to a book-specific heat capacity.

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Gas backdrop, fundamental equations of state and stage relationships

Jingfa Li , Bo Yu , in Sustainable Natural Gas Reservoir and Product Engineering, 2022

iii.6 Specific heat chapters of natural gas

The specific heat capacity at abiding book and pressure of an compatible compressible organisation can be respectively defined every bit [20, 21],

(32) $c_5={\left(\frac{\partial u}{\partial T}\right)}_v,c_p={\left(\frac{\partial h}{\partial T}\right)}_p$

where, u is the internal energy of arrangement, kJ/kmol; h is the enthalpy of system, kJ/kmol.

It is known from the laws of thermodynamics for an ideal gas that,

(33) $c_p^0-c_v^0=R$

For a real gas, the applicative relationship is,

(34) $c_p-c_v=\frac{T{\left(\frac{\partial p}{\partial T}\right)}_{\rho }^{\mathrm{ii}}}{{\rho }^2{\left(\frac{\partial p}{\partial \rho }\right)}_T}$

For an ideal gas component i, the specific oestrus capacity at constant pressure tin be derived as follows,

(35) $c_{\mathit{pi}}^0=B_i+\mathrm{two}{C}_{i}T+3D_i{T}^2+\mathrm{four}{E}_i{T}^3+\mathrm{five}{F}_i{T}^{\mathrm{iv}}$

where, B _i , C _i , D _i , E _i , F _i are constants related to component i.

For an ideal gas mixture,

(36) $c_p^0=\sum _i{y}_i{c}_{\mathit{pi}}^0$

For a existent gas, the specific heat capacity at abiding book tin exist calculated by,

(37) $c_{\mathrm{five}}=c_v^0+{\int }_0^{\rho }{\left(\frac{\partial c_v}{\partial \rho }\right)}_T\mathrm{d}\rho =c_v^0+{\int }_0^{\rho }\left[-\frac{T}{{\rho }^{\mathrm{ii}}}{\left(\frac{{\partial }^{2}p}{\partial T^2}\right)}_{\rho }\right]\mathrm{d}\rho$

Substituting the EOS of natural gas into Eq. (37) tin can yield the specific heat chapters at constant book (Table 4). Co-ordinate to the relation between c _v and c _p (run across Eq. (34)), the specific heat chapters at constant pressure can also be easily calculated.

Table four. Calculation formulas for specific heat capacity of natural gas.

EOS	Calculation formulas for specific oestrus capacity
RK	$c_v=c_v^0+\frac{0.5a}{{\mathit{bT}}^{0.5}}ln\left(1+\mathit{b\rho }\right)$
SRK	$c_{\mathrm{five}}=c_v^0+\frac{{\mathrm{d}}^{\mathrm{ii}}a}{\mathrm{d}{T}^2}\frac{T}{b}ln\left(\mathrm{i}+\mathit{b\rho }\right)$
PR	$c_v=c_v^0-\frac{T}{2\sqrt{2}b}\frac{{\mathrm{d}}^{2}a}{\mathrm{d}{T}^2}ln\left[\frac{1+\left(\mathrm{ane}+\sqrt{\mathrm{ii}}\right)\mathit{b\rho }}{1+\left(1-\sqrt{\mathrm{ii}}\right)\mathit{b\rho }}\right]$
BWRS	$c_v=c_v^0+\left(\frac{6C_0}{T^3}-\frac{12D_0}{T^4}+\frac{20{\mathrm{Due\; east}}_0}{T^{\mathrm{v}}}\right)\rho +\frac{d}{T^2}{\rho }^2-\frac{2\mathit{\alpha d}}{5T^2}{\rho }^5+\frac{3c}{\gamma T^3}\left[\left({\mathit{\gamma \rho }}^{\mathrm{ii}}+2\right){\mathrm{due\; east}}^{-{\mathit{\gamma \rho }}^2}-\mathrm{two}\right]$

The ratio of the specific heat capacity at constant force per unit area to that at abiding book is called the heat capacity ratio,

(38) $\mathrm{chiliad}=\frac{c_p}{c_v}$

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From Thermostatics to Non-equilibrium Thermodynamics

Michel Feidt , in Finite Physical Dimensions Optimal Thermodynamics 1, 2017

1.3.i Calorimetry and calorimetric coefficients

1.3.i.1 Standard definitions

Up to a second order, the expression of elementary rut exchanged when passing from an equilibrium land to an infinitely shut equilibrium state takes one of the post-obit forms:

[1.xix] $\delta Q=C_{5}dT+l_{T}dV$

[1.20] $\delta Q=C_{P}dT+h_{T}dP$

[one.21] $\delta Q={\lambda }_{V}dP+{\mu }_{P}dV$

The vi calorimetric coefficients involved in these 3 equations are characteristic to the thermodynamic system. When considered with respect to unit of measurement mass, these same coefficients are called specific coefficients; they intrinsically characterize pure substances. These various coefficients are interrelated.

Since dU, dH and dS are total differentials, they pb to Clapeyron relations:

[1.22] $l_T=T{\left(\frac{\partial P}{\partial T}\right)}_V$

[1.23] $h_T=-T{\left(\frac{\partial V}{\partial T}\right)}_P$

then the generalized Mayer'southward relation:

[ane.24] $C_P-C_5=T{\left(\frac{\partial P}{\partial T}\right)}_V{\left(\frac{\partial V}{\partial T}\right)}_P$

Annotation

$\gamma =\raisebox{1ex}{$C_P$}\!\left/ \!\raisebox{-1ex}{$C_V$}\right.$ .

ane.3.1.2 General definition

Specific heat capacity is the amount of estrus to be supplied to (or taken out of) the unit mass of a organization in club to increase (or subtract) its temperature past one degree in a thermodynamic process in which quantity X is imposed, co-ordinate to:

[1.25] $\delta Q=C_{X}dT$

Permit us note that the heat involved in the process corresponds to a sensible heat. A 2d type of heat is the latent oestrus; it is feature to phase changes. Vaporization and condensation latent heats play a very important role in many engines.

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Thermodynamics and heat transfer

J. Carvill , in Mechanical Engineer's Data Handbook, 1993

3.four.four Specific rut capacities

Specific heat capacity of solids and liquids (kJ kg ^{− i} Grand^{− i})

Aluminium	0.897	Oil, machine	1.676
Aluminium bronze	0.897	Paraffin	ii.100
Brass	0.377	Methane series wax	2.140
Bronze	0.343	Petroleum	two.140
Cadmium	0.235	Phosphorus	0.796
Constantan	0.410	Platinum	0.133
Copper	0.384	Prophylactic	2.010
Ethanol	two.940	Common salt, common	0.880
(ethyl alcohol)		Sand	0.796
Glass: crown	0.670	Seawater	3.940
flint	0.503	Silica	0.800
Pyrex	0.753	Silicon	0.737
Gold	0.129	Silverish	0.236
Graphite	0.838	Tin	0.220
Ice	2.100	Titanium	0.523
Iron: cast	0.420	Tungsten	0.142
pure	0.447	Turpentine	ane.760
Kerosene	two.100	Uranium	0.116
Atomic number 82	0.130	Vanadium	0.482
Magnesia	0.930	Water	iv.196
Magnesium	one.030	Water, heavy	4.221
Mercury	0.138	Wood (typical)	2.0 to
Molybdenum	0.272		3.0
Nickel	0.457	Zinc	0.388

Specific oestrus capacity of gases, gas constant and molecular weight (at normal pressure and temperature)

Gas	Specific heats c p	(kJ kg−one Thou−1) c five	$\gamma =\frac{c_p}{c_5}$	Gas constant, R (kJ kg−1Thousand−1)	Molecular weight, Yard
Air	1.005	0.718	1.4	0.2871	28.96
Ammonia	2.191	one.663	1.32	0.528	15.75
Argon	0.5234	0.3136	ane.668	0.2081	40
Butane	i.68	1.51	i.11	0.17	58
Carbon dioxide	0.8457	0.6573	1.29	0.1889	44
Carbon monoxide	ane.041	0.7449	1.398	0.2968	28
Chlorine	0.511	0.383	ane.33	0.128	65
Ethane	ane.7668	1.4947	1.eighteen	0.2765	thirty
Helium	v.234	3.1568	1.659	2.077	iv
Hydrogen	14.323	10.1965	1.405	4.124	ii
Hydrogen chloride	0.813	0.583	1.40	0.230	36.15
Marsh gas	2.2316	1.7124	1.thirty	0.5183	16
Nitrogen	1.040	0.7436	1.twoscore	0.2968	28
Nitrous oxide	0.928	0.708	1.31	0.220	37.8
Oxygen	0.9182	0.6586	one.394	0.2598	32
Propane	1.6915	ane.507	i.12	0.1886	44
Sulphur dioxide	0.6448	0.5150	ane.25	0.1298	64

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Polymer Characterization

C. Schick , in Polymer Science: A Comprehensive Reference, 2012

ii.31.ii.ii.one Linear browse

The most mutual mode of operation in DSC is heating or cooling at abiding rates. The primary outcome of such an experiment is a plot of the heat flow charge per unit versus fourth dimension. If the temperature of the sample position is known, then data can likewise be represented as the heat flow rate versus temperature. (One should know that generally a temperature near the sample is measured and not the sample temperature itself.) Figure 2 shows a typical example.

Figure 2. Temperature profile and measured heat menstruation charge per unit for (a) empty pans, (b) sapphire calibration standard (31.3   mg), and (c) initially baggy PEEK (29   mg). Heating rate β  =   20   Yard   min⁻¹.

Data from PerkinElmer Pyris Diamond DSC. Reproduced with permission from Schick, C. Anal. Bioanal. Chem. 2009, 395, 1589–1611. ³⁵

From the heat period rate curves shown in Figure 2 , specific estrus capacity c _p(T) can be obtained as follows

[viii] $c_{\text{p}}(T)=c_{\text{p},\text{sapphire}}(T)\frac{m_{\text{sapphire}}\beta }{m_{\text{sample}}\beta }\frac{{\Phi }_{\text{sample}}(T)-{\Phi }_{\text{empty}}(T)}{{\Phi }_{\text{sapphire}}(T)-{\Phi }_{\text{empty}}(T)}=K(T)\frac{{\Phi }_{\text{sample}}(T)-{\Phi }_{\text{empty}}(T)}{m_{\text{sample}}\beta }$

with

$\mathrm{Grand}(T)=c_{\text{p},\text{sapphire}}(T)\frac{{\mathrm{grand}}_{\text{sapphire}}\beta }{{\Phi }_{\text{sapphire}}(T)-{\Phi }_{\text{empty}}(T)}$

where K(T) is a temperature-dependent calibration gene, which can be stored for future use. Hither, all measurements are nerveless at the aforementioned scanning rate. The isotherms at the beginning and the stop of the scan are used to correct for small changes in oestrus losses between empty, sapphire, and sample measurements by adjustment these parts of the curves. Small changes in losses are unavoidable, because the thermal properties, such as thermal electrical conductivity, of the samples are different. On the other hand, inspection of the heat flow rate at the isotherms allows u.s. to cheque the correct placement and thermal contacts of all the parts of the measuring system moved during sample changes. Especially the high temperature isotherm should not vary as well much betwixt successive measurements.

Specific heat capacity is the well-nigh useful quantity bachelor from DSC considering it is directly related to sample properties and, according to eqns [1]–[five], directly linked to stability and guild. Nevertheless, often just estrus menstruum rate, as obtained from a unmarried sample measurement, is presented. There are several reasons why this should not be presented:

i.

Each heat flow rate graph needs indication of endothermic or exothermic management because plot direction is not standardized.

two.

Curves measured at different scanning rates are not easy to compare.

3.

If not divided by the sample mass, curves for different samples cannot be compared.

four.

If empty pan measurements are not subtracted, traces may be curved and baseline structure for peak integration may be difficult.

5.

If the oestrus flow rate calibration factor G(T) is temperature dependent, the obtained heat of fusions and other such parameters may exist erroneous.

Performing corrections (3)–(5) yields specific heat capacity as given by eqn [8]. Because most of the DSC software packages include determination of specific heat capacity according to eqn [8], it is strongly recommended to determine specific heat capacity and not to present heat catamenia rate curves. Even though presenting specific rut capacity data is preferable, at that place may be reasons not to do so. The normalization of the heat flow rate curve by the browse charge per unit and the sample mass may result in 'pseudo c _p measurements', which can be used to determine temperature-dependent crystallinity and other quantities as shown in Reference 8. But there is another very strong argument in favor of presenting specific oestrus capacity rather than 'pseudo c _p' or heat flow charge per unit. For more than 200 polymers, specific heat chapters data from 0 to 1000   K are available from the ATHAS Data Bank (ATHAS-DB). ³⁶ The data can be used for a comparison of measured data in the glassy or liquid state with the recommended values. This allows an easy bank check of the quality of the measured information, although 1 should keep in mind that the accuracy of the recommended information bank data is only about 6%. Figure 3 shows specific rut chapters (according to eqn [8]) calculated from the information shown in Figure 2 .

Figure 3. Specific heat capacity versus temperature for an initially amorphous PEEK sample. Data from Effigy 2 . Reference information (straight lines) for the fully amorphous (liquid) and crystalline (solid) PEEK are available from the ATHAS-DB. ³⁶

Reproduced with permission from Schick, C. Anal. Bioanal. Chem. 2009, 395, 1589–1611. ³⁵

A more detailed discussion of the evaluation of the curves shown in Effigy 3 is given in Reference 35.

Besides scan measurements on heating, DSC allows cooling in a wide range of cooling rates. Depending on the instrument and the temperature range of interest, cooling rates up to 750   K   min⁻¹ may be reached (HyperDSC™ PerkinElmer, Usa). ^20,37–39 But more often than not the temperature range for controlled cooling at the highest rates is limited. Measurements performed in a wide range of heating or cooling rates require an optimization of the experimental weather condition. The sample mass should scale inversely with the scanning charge per unit. At depression rates when the thermal lag is not an effect, the sample mass should be high to have a good signal-to-dissonance ratio. At high rates when signals are large, the sample mass should exist small to minimize the heat flow to the sample, which is proportional to the rate and causes the thermal lag. Problems related to thermal lag, temperature calibration, and reproducibility in fast scanning DSC experiments were intensively studied and adequate recommendations were made. ^37,40,41 Figure 4 shows cooling curves in the crystallization range of depression-density polyethylene (PE). At rates college than 200   K   min⁻ⁱ, controlled cooling down to 100   °C was not possible because of the limited cooling power of the used mechanical intercooler. If higher cooling rates are needed, liquid nitrogen has to be used. For the lower scanning rates shown in Figure 4 , the sample mass must be large enough to ensure a expert indicate-to-dissonance ratio. For higher rates, the large sample (iv   mg) causes some thermal lag, as discussed in the textbooks and References 37, xl, and 42. It is likewise seen in the broadening of the crystallization top at 20   Grand   min^−one compared with the 0.4   mg sample at the same cooling charge per unit. Data every bit shown in Effigy 4 provide data nearly crystallization kinetics and can be analyzed past using unlike kinetic models. ^43–48

Figure iv. Cooling curves in the crystallization range of low-density PE. Samples are of mass 4   mg in a 25   mg aluminum pan for cooling rates upwardly to −20   K   min⁻¹ and of mass 0.4   mg in 2   mg aluminum foil for higher cooling rates. Heat capacity is plotted downward.

Data from PerkinElmer Pyris i DSC. Reproduced with permission from Schick, C. Anal. Bioanal. Chem. 2009, 395, 1589–1611. ³⁵

Equally shown in Figure iv , DSC has a broad dynamic range that tin can be extended at to the lowest degree past one society of magnitude toward lower rates; in this way it covers 3 orders of magnitude. An extension by several orders of magnitude toward higher rates is discussed in Department 2.31.iii.ii. The possibility of cooling a sample reasonably fast allows u.s.a. to study the construction germination in far-from-equilibrium situations such every bit 'quasi'-isothermal crystallization at deep undercooling.

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Cloth Interface of Pantograph and Contact Line

Jiqin Wu , in Pantograph and Contact Line Organization, 2018

5.2.3 Thermal Performance

When selecting materials for strip and contact wire, the thermal performance of the material will too be considered. The pantograph and overhead contact line system works in a strong electric current environs. Joule heat, arc heat, and friction heat acquired past current flowing through the pantograph and overhead contact line contact point volition lead to temperature rise of strip and contact wire. Excessive temperature rise will bring negative impact to performance of strip and contact wire fabric.

Specific rut capacity, thermal expansion, heat conduction, thermal radiations, and thermoelectric strength are all aspects of thermal performance.

5.2.three.i Specific estrus chapters

Specific rut capacity is the energy required to increment temperature of textile of a certain mass by 1°C, in the unit of measurement of J/(kg·Chiliad). Table 5.ii lists the specific heat capacity of several materials.

Table 5.2. Specific Heat Capacities of Several Materials (25°C)

Materials	Specific Heat Capacities [J/(kg·K)]
Aluminum	900
Copper	389
Silver	235
Contumely	375
Carbon	710

5.two.3.2 Thermal expansion

Expansion and contraction of a substance is a common phenomenon. The expansion coefficient is a parameter indicating such belongings. Commonly, the expansion coefficient refers to length variation of a material per unit length under temperature variation by 1K, and then information technology is also called the linear expansion coefficient (1/One thousand) to be distinguished from the volume expansion coefficient indicating book variation of material in unit book. Tabular array 5.three lists linear expansion coefficients of some materials.

Table v.3. Linear Expansion Coefficients of Some Materials (25°C)

Materials	Linear Expansion Coefficients (×0.000001/°C)
Ordinary cast iron	ix.2–11.eight
Iron	12–12.5
Copper	18.5
Bronze	17.5
Brass	xviii.5
Aluminum blend	23.8

5.2.three.3 Heat conduction

Applying thermal vibration with more energy from outside to a mass point in thermal vibration at sure temperatures volition atomic number 82 to an increase of thermal vibration of adjacent mass points. In such cases, the wave height with higher thermal vibration moves to low temperature to transfer large thermal vibration introduced at showtime via the mass point. This phenomenon is oestrus conduction, namely free energy migration generated by temperature deviation between adjacent parts of a cloth. The abiding representing the heat conduction ability of material is called estrus conductivity or heat electrical conductivity coefficient, in West/(chiliad·1000), namely the heat transferred through unit horizontal cross-sectional area in unit time when at vertical temperature slope of 1°C/m.

Table 5.4 lists the heat conductivity of some materials at normal temperature.

Table 5.4. Oestrus Conductivities of Several Materials (25°C)

Materials	Rut Conductivities [×4.ii × 102West/(grand·M)]
Copper	0.927
Contumely	0.26
Aluminum	0.488
Carbon	129

Metal is a good conductor of electricity and oestrus. This is because gratuitous electrons be in metal. Collisions betwixt costless electrons become more and more frequent with a ascension of temperature, and their movement will become difficult. So, heat electrical conductivity of metal reduces with a rise of temperature. Impurity in metal will obstruct the motion of gratis electrons and reduce conductivity, then heat electrical conductivity of alloys is significantly lower, equivalent to 15%–70% of the base phase metal.

5.two.three.iv Estrus resistance

Rut resistance is an important property in cloth awarding. The melting point of a material tin reflect the heat resistance of the material. The temperature at fusion welding is called the melting point. Usually, the larger the intermolecular force in a material's structure, the higher the melting point will be. Table 5.five lists the melting points of several materials.

Tabular array 5.5. Melting Points of Several Materials

Materials	Melting Points (°C)
Copper	1083
Steel	1515
Aluminum	660
Graphite	≈3700

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Further Considerations in Field Modeling

In Computational Fluid Dynamics in Burn down Engineering, 2009

Specific Heat Capacity of Dry out Virgin Forest

The specific heat chapters of dry virgin wood as a part of temperature has been determined by Atreya (1983) for a temperature range from 0°C to 140°C. Fredlund (1988) has assumed that the human relationship is valid even for temperatures above 140°C. The expression for the specific heat capacity of dry virgin forest as a linear part of temperature is given by

(4.11.37) $C_{\mathit{pw}}=C_{\mathit{pw},o}+C_{\mathit{prisoner\; of\; war},m}{T}_s$

where C _pw,o = 1.4 kJ kg^−one Grand⁻ⁱ and C _{prisoner of war,grand} = 3.0 × 10^−four kJ kg⁻¹ K⁻². It is nonetheless noted that a constant specific estrus capacity for dry virgin wood independent of temperature has as well been assumed by a number of investigators such as Kanury and Blackshear (1970a), Kung (1972), Kung and Kalelkar (1973), Chan et al. (1985), Alves and Figueiredo (1989), Bonnefoy et al. (1993), and Di Blasi (1994a). Values ranging from ane.386 kJ kg^−ane K⁻¹ to 2.52 kJ kg^−one Grand⁻¹ with most of them larger than ii.0 kJ kg⁻¹ Thousand⁻ⁱ have been typically employed.

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Principles of CSP performance assessment

N. Janotte , ... L. Ramirez , in The Performance of Full-bodied Solar Power (CSP) Systems, 2017

Estrus chapters

The specific estrus capacity or enthalpy of the HTF is essential for the heat and enthalpy balances of any system nether investigation. The useful heat derived from measured temperatures and menses rates is directly proportional to these values. Differential scanning calorimeters are standard laboratory instruments used for determining the specific oestrus capacity of HTFs in CSP applications [ iv]. Particular measurement challenges effect from the typical evaporation of thermal oils at ambient pressure and the temperature range of their application. To some extent, these can be overcome using Calvet DSC with a iii-dimensional detector encompassing the sample. If evaporation is not prevented, data across the boiling temperature has to be extrapolated. An alternative, truly measuring at operational weather condition, lies in using an adiabatic menses calorimeter and thus evaluating the enthalpy balance of a small quantity of the HTF in a featherbed of the system [5]. Unlike differential scanning calorimeters, adiabatic catamenia calorimeters are not commercially available, and imply considerably higher instrumental and operational expense.

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Thermophysical Properties of Nanofluids

I.M. Mahbubul , in Preparation, Characterization, Properties and Application of Nanofluid, 2019

4.5.v Result of Preparation Method on Specific Estrus

Mostly, specific oestrus capacities of fluids are measured by using different types of differential scanning calorimeter (DSC). Based on the measurement principle of DSC, information technology analyzes a very small amount of liquid, which can exist every bit much equally in the milligram (mg) calibration (about v mg). It is very hard to differentiate the effect of an ultrasonication menstruum (or other variation) during nanofluid preparation by considering just a fraction of mg of fluid. Therefore, the event of ultrasonication on the specific heat capacity of nanofluid was non considered for analysis.

[This department (four.5 Specific Rut) is adjusted from Shahrul et al. (2014), copyright (2014), with permission from Elsevier.]

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Investigation of Irreversibility With CO2 Emission Measurement in Industrial Enamel Furnace

Sedat Vatandas , ... Mehmet Z. Söğüt , in Exergetic, Energetic and Environmental Dimensions, 2018

Nomenclature

c_p

Specific heat capacity, kJ/kg  K

thousand

Gravity, m/southwardⁱⁱ

h

Enthalpy, kJ/kg

I

Irreversibility, kJ/h

$\dot{m}$

Mass flow, kg/h

$\dot{E}$

Energy, kJ/h

$\dot{E}x$

Exergy, kJ/h

$\dot{E}{\mathrm{10}}_i$

Exergy catamenia, kJ/h

$\dot{\mathrm{East}}{x}_{che}$

Chemic exergy, kJ/h

$\dot{\mathrm{Due\; east}}{\mathrm{ten}}_{ki\mathrm{northward}}$

Kinetic exergy, kJ/h

$\dot{E}{x}_{ph}$

Physical exergy, kJ/h

$\dot{E}{x}_{pot}$

Potential exergy, kJ/h

$IP$

Improvement potential, kJ/h

south

Entropy, kJ/kg   K

$\dot{\mathrm{Due\; west}}$

Piece of work, kJ/h

$\dot{Q}$

Heat, kJ/h

Z

Geopotential height, 1000

$\psi$

Flow exergy, kJ/kg

μ

Efficiency

${\omega }_{\mathrm{C}{\mathrm{O}}_2}$

CO₂ emission coefficient

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Why Is Specific Heat Important,

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