Specific heat

Specific Heat.—Equal volumes of different substances at the same temperature contain different amounts of heat. If two 

The amount of heat required to raise a kilo of water from 0° C. to-1° C. is the unit of heat, and is known as a calorie. The specific heat of any substance is the amount of heat required to raise one kilo of that substance 1° in temperature, expressed in calories. 

Specific heat curves for selected polymers of the three general polymer categories. 

For filled polymer systems with inorganic and powdery fillers, a rule of mixtures1 can be written as 

Specific heat (Cp, in J/g K) of vegetable oil is influenced by temperature (Formo 1979) as described in the following equation  

Liquid specific heat capacity for fatty acids, triacylglycerols, and vegetable oils was estimated based on their fatty acid composition (Morad et al. 2000). A Rowlinson-Bondi equation was used to estimate specific heat (Cp) for pure fatty acid. The liquid specific heat capacities of oils were estimated by using mixture properties corresponding to the fatty acid composition and a correction factor, which accounts for the TAG form. The Rowlinson-Bondi equation used is as follows  

The constants a, b, c and d for various chemical groups were used to calculate the ideal gas capacity for pure fatty acids. The reduced temperature is calculated 

A factor was used to correct the difference between calculated and experimental values as derived from Morad s study. For MW 850, as in our sample, 

The accuracy of Morad s estimation method was determined to be 5%. This model was used by Wang and Briggs (in press) to estimate Cp of soybean oils with modified fatty acid composition at various temperatures. All oils had the same slope of 0.0024, but the constant ranged from 1.7992 to 1.8583, compared with a slope of 0.0026 and a constant of 1.9330 from Formo s equation. 

Specific heat is defined as the energy needed to raise the temperature of a unit mass by a unit degree temperature. For constant volume process 5zv = pdv = 0 and the first law reduces to 8Q = dLf. The constant volume specific heat is expressed as 

For a constant pressure process, 5w = pdv and the first law reduces to 5Q dLf + PdV = dH. The constant pressure specific heat is expressed as 

The specific heat (C) is the amount of energy required, per unit mass or per mole, to raise the temperature of a substance by one degree. This is the derivative of its internal energy dU/dT, and since magnetic levels make a contribution to this their separations can in principle be measured from C(T) measurements. However, the magnetic contribution to the specific heat must be disentangled from that of lattice vibrational modes. 

the level splitting can be determined in the absence of an applied magnetic field. Alternatively, a field can be applied to induce the splittings to be determined. 

The specific heat of diamond is generally comparable to that of graphite and is higherthan most metals (see Ch. 3, Sec. 4.3 and Table 3.5). The specific heat of diamond, like that of all elements, increases with temperature (see Table 11.3). 

The specific heat is a function of temperature. A significant rise in the specific heat is observed near 

Specific heat and enthalpy control the cooling of an article in a mould and predominantly the design of the cooling channels in a mould. The cooling system should balance the heat flow from the part to ensure uniform part cooling and minimise residual stresses, differential shrinkage, and warpage. 

The heat capacity at constant pressure (c ), at various temperatures, is given in Table 3.6. 

3 Glass Transition Temperature and Melting/Crystallisation Temperature 

Drawn from the data in Handbook of Polyolefins Synthesis and Properties, 1st Edition, Eds., C. Vasile and R.B. Seymour, Marcel Dekker, New York, NY, USA, 1993. Copyright Marcel Dekker, 1993. 

The specific heat data for pure ZnO were further analyzed by considering two non-Debye features at different temperature regions according to 

Room-Temperature Specific Heat Values for Various Engineering Materials 

Sources ASM Handbooks, Volumes 1 and 2, Engineered Materials Handbooks, Volumes 1, 2, and 4, Metals Handbook Properties and Selection Nonferrous Alloys and Pure Metals, Vol. 2, 9th edition, and Advanced Materials Processes, Vol 146, No. 4, ASM International, Materials Park, OH Modern Plastics Encyclopedia 1977-1978, The McGraw-Hill Companies, New York, NY and manufacturers technical data sheets. 

METALS AND METAL ALLOYS Plain Carbon and Low-Alloy Steels 

As shown already, specific heat is the quantity of heat required to raise the unit mass of the material through 1°C, that is, the heat capacity of unit mass. There is the specific heat at constant volume which is virtually impossible to measure, and the specific heat at constant pressure, which is the quantity normally measured. The difference between the two specific heats is usually small enough to be ignored. In fact, the heat capacity at constant volume per unit volume is given by p C, so that it is found  

Except where the very highest precision is required when an adiabatic calorimeter would be used, specific heat can be measured using differential scanning calorimetry 

Measurement of the specific heat at Tc should yield quite informative data. Information can be gained about the binding energy of the electrons in the Cooper pairs as mediated by electron-phonon coupling (in the BCS theory). 

The original specific heat experiments on BaPb xB Og by Methfessel et al (60) immediately raised the prospect that an unusual mechanism was operative in this newly found system. Their finding of no heat capacity anomaly at Tc could actually have a number of possible interpretations, including an impurity phase giving rise to superconductivity, a non-phonon mechanism, or some new form of conductivity. 

More recent measurements have shown (61)(62) that the problem with the experiment was that the thermal effect at Tc is actually very small. In fact, after the true heat had been determined, research was (and still is) directed toward finding out why the Tc is so high (63). The Sommerfeld parameter or electronic specific heat parameter appears to be identical (1.5mJ/mol K2) in BaPbj B Og 

Ranade and co-workers [48] showed that PAI-montmorillonite nanocomposites had a distinctly reduced specific heat when compared to clay free polymer. 

Various techniques discussed in the next sections have been used to measure the specific heat of polymers. 

When a body absorbs heat, the first effect observed is an increase in temperatme. Thus, each material has a different heat behavior. These differences in behavior are reflected in a magnitude characteristic of each substance called specific heat. 

The specific heat c is defined as the amoimt of heat to be absorbed by 1 gram of a substance to raise its temperature 1 °C.  

if a mass m of a substance undergoes a temperature change AT, AQ heat absorbed or transferred to the substance is 

Specific heat behavior in crystalline solids can be characterized by the following three laws law of Dulong and Petit, law of Debye, and Einsteins law. 

These laws apply to regular solid (crystalline). However, the solids exposed in this work are generally non-crystalline, so that the above results would not be more than a first approximation. 

rotational energy, e, vibrational energy, 8, electronic energy, e, and their interaction energy, 8  

A molecule containing n atoms has 3n degrees of freedom of mohon in space  

When the temperature of a molecule is increased, rotational and vibrational modes are excited and the internal energy is increased. The excitation of each degree of freedom as a function of temperature can be calculated by way of statis-hcal mechanics. Though the translational and rotational modes of a molecule are fully excited at low temperatures, the vibrational modes only become excited above room temperature. The excitation of electrons and interaction modes usually only occurs at well above combushon temperatures. Nevertheless, dissocia-hon and ionization of molecules can occur when the combustion temperature is very high. 

When the translational, rotahonal, and vibrational modes of monatomic, diatomic, and polyatomic molecules are fully excited, the energies of the molecules are given by 

Since the specific heat at constant volume is given by the temperature derivative of the internal energy as defined in Eq. (1.7), the specific heat ofa molecule, is represented by 

As the temperature of a substance is raised, energy must be put into it to enable the molecules of the substance to move more rapidly relative to each other and to 

The heat required to raise the temperature of a substance is called the specific heat, defined as the amount of heat energy required to raise the temperature of 1 g of substance by 1°C. It can be expressed by file equation 

This equation can be used to calculate quantities of heat used in increasing water temperature or released when water temperature decreases. As an example, consider the amount of heat required to raise the temperature of 11.6 g of liquid water from 14.3°C to 21.8°C  

Details are given in Table 16.1 for carrying out measurements to ASTM and DIN standards. 

The burning of 1.0 g of coal produces 8.4 kcal. How many kilojoules are produced  

LEARNING GOAL Identify energy as potential or kinetic convert between units of energy 

21 Discuss the changes in the potential and kinetic energy of a roller-coaster ride as the roller coaster chmbs to the top and goes down the other side. 

23 Indicate whether each of the following statements describes potential or kinetic energy  

A person loses weight when food intake is less than energy output. Many diet products contain cellulose, which has no nutritive 

29 Using the energy values for foods (see Table 3.7), determine 331 

Using the energy values for foods (see Table 3.7), determine each of the following (round off the answers in kilocalories or kilojoules to the tens place)  

One cup of clam chowder contains 16 g of carbohydrate, 12 g of fat, and 9 g of protein. How much energy, in kilocalories and kilojoules, is in the clam chowder (Round off the kilocalories or kilojoules to the tens place.) 

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Reactor heat carrier. Also as pointed out in Sec. 2.6, if adiabatic operation is not possible and it is not possible to control temperature by direct heat transfer, then an inert material can be introduced to the reactor to increase its heat capacity flow rate (i.e., product of mass flow rate and specific heat capacity) and to reduce... 

Calculate the capital cost target for the mixed specification heat exchanger network from Eq. (7.21) using the cost law coefficients for the reference specification. 

Example 9.1 A process involves the use of benzene as a liquid under pressure. The temperature can be varied over a range. Compare the fire and explosion hazards of operating with a liquid process inventory of 1000 kmol at 100 and 150°C based on the theoretical combustion energy resulting from catastrophic failure of the equipment. The normal boiling point of benzene is 80°C, the latent heat of vaporization is 31,000 kJ kmol the specific heat capacity is 150 kJkmoh °C , and the heat of combustion is 3.2 x 10 kJkmok. ... 

British thermal unit (Btu) The most commonly used industrial heal unit the amount of heat required to raise 1 lb of water through UF under specified conditions. Since the specific heat of water varies, particularly with temperature, the actual value of Btu is dependent on the conditions chosen as stan-... 

In statistical mechanics (e.g. the theory of specific heats of gases) a degree of freedom means an independent mode of absorbing energy by movement of atoms. Thus a mon-... 

Dulong and Pedt s law The product of the atomic weight and the specific heat of a metal is constant of value approximately 6-2. Although not true for all metals at ordinary temperatures, these metals and several non-metals approximate to the law at high temperatures. 

The thermal properties of an ideal gas, enthalpy, entropy and specific heat, can be estimated using the method published by Rihani and Doraiswamy in 1965 ... 

For non-polar components like hydrocarbons, the results are very satisfactory for calculations of vapor pressure, density, enthalpy, and specific, heat and reasonably close for viscosity and conductivity provided that is greater than 0.10. 

The specific heat for a liquid at constant pressure, written as and expressed in kJ/(kg-K), can be calculated for mixtures in two ways ... 

The isobaric specific heat for a petroleum fraction is estimated by a correlation attributed to Watson and Nelson in 1933, which was used again by. Johnson and Grayson in 1961 as well as by Lee and Kesler in 1975. This relation is valid at low pressures i... 

Cpi = specific heat of the liquid C pi = specific heat of the liquid whose is 11.8... 

The specific heat of gases at constant pressure is calculated using the principle of corresponding states. The for a mixture in the gaseous state is equal to the sum of the C g of the ideal gas and a pressure correction term ... 

Hgp = specific enthalpy of the ideal gas Cpgp = specific heat of the ideal gas... 

Agp = conductivity of the ideal gas pgp specific heat of the ideal gas = critical pressure M = molecular weight... 

C , = average specific heat of the pure liquid between... 

Figure A2.2.2. The rotational-vibrational specific heat, C, of the diatomic gases HD, HT and DT as a fiinction of temperature. From Statistical Mechanics by Raj Pathria. Reprinted by pennission of Butterwortii Heinemann.

Fluctuations of observables from their average values, unless the observables are constants of motion, are especially important, since they are related to the response fiinctions of the system. For example, the constant volume specific heat of a fluid is a response function related to the fluctuations in the energy of a system at constant N, V and T, where A is the number of particles in a volume V at temperature T. Similarly, fluctuations in the number density (p = N/V) of an open system at constant p, V and T, where p is the chemical potential, are related to the isothemial compressibility iCp which is another response fiinction. Temperature-dependent fluctuations characterize the dynamic equilibrium of themiodynamic systems, in contrast to the equilibrium of purely mechanical bodies in which fluctuations are absent. 

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