Units of heat capacity

Analysing Equations (3.6) and (3.7) helps us remember how the SI unit of heat capacity Cy is J K-1. Chemists usually cite a heat capacity after dividing it by the amount of material, calling it the specific heat capacity, either in terms of J K-1 mol-1 or J K-1g-1. As an example, the heat capacity of water is 4.18 J K-1g-1, which means that the temperature of 1 g of water increases by 1 K for every 4.18 J of energy absorbed. 

JOULE PER KELVIN (J/K). A unit of heat capacity urul entropy. 

In general, heat capacity equations are valid only over a moderate range of temperatures. Table 2.1 gives constants to be used with Equation 2.28 for air and water gases. The units of heat capacity with these constants are cal/(g-mole)(°K or °C) or Btu/(lb-mole)(°R or °F). 

The SI units of heat capacity are J/K, as can be easily seen from the definition of C. Heat capacity is an extensive property of matter. That is, larger samples have greater heat capacities. 

Usually we use calories per gram per Kelvin, or BTU per pound per degree Rankine as units of heat capacity. Numerically, the two groups of units are identical. We also use heat capacity on a molar basis, in which case the units are per gram mole or per pound mole, and again these are numerically identical. 

Heat capacity (specific heat) n. The amount of heat required to raise the temperature of a unit mass of a substance one degree. In the SI system, the unit of heat capacity is J/kgK, but kJ/kgK, or J/gK are often more convenient. Conversions from older units are 1 cal/g°C = 1 Btu/lb°F = 4.186 J/ gK. Most neat resins have heat capacities (averaged from room temperature to about 100°C) between 0.92J/gK for polychloro-trifluoroethylene and 2.9 for polyolefins (The heat capacity of water, one of the highest of all materials, is 4.18J/gK at room temperature.) A term loosely used as a synonymous with heat capacity but not truly so is specific heat. 

Joule per kelvin J/K SI unit of heat capacity and entropy. 

Notice that the higher the heat capacity of a system, the smaller the change in temperature for a given amount of absorbed heat. We define the heat capacity (C) of a system as the quantity of heat required to change its temperature by 1 °C. As we can see by solving Equation 6.5 for heat capacity, the units of heat capacity are those of heat (typically J) divided by those of temperature (typically °C). 

The heat capacity of a subshince is defined as the quantity of heat required to raise tlie temperature of tliat substance by 1° the specific heat capacity is the heat capacity on a unit mass basis. The term specific heat is frequently used in place of specific heat capacity. This is not strictly correct because traditionally, specific heal luis been defined as tlie ratio of the heat capacity of a substance to the heat capacity of water. However, since the specific heat of water is approxinuitely 1 cal/g-°C or 1 Btiiyib-°F, the term specific heal luis come to imply heat capacity per unit mass. For gases, tlie addition of heat to cause tlie 1° tempcniture rise m iy be accomplished either at constant pressure or at constant volume. Since the mnounts of heat necessary are different for tlie two cases, subscripts are used to identify which heat capacity is being used - Cp for constant pressure or Cv for constant volume. Tliis distinction does not have to be made for liquids and solids since tliere is little difference between tlie two. Values of heat capacity arc available in the literature. ... 

If Q units of heat are required to raise the temperature of a body 1°, then 2Q will be required to raise the temperature of two such bodies through 1°, and so on. Hence the heat capacity of a homogeneous body is proportional to its mass. The heat capacity of unit mass of a homogeneous body may therefore be... 

In the SI system, the unit of heat is taken as the same as that of mechanical energy and is therefore the Joule. For water at 298 K (the datum used for many definitions), the specific heat capacity Cp is 4186.8 J/kg K. 

Prior to the now almost universal adoption of the SI system of units, the unit of heat was defined as the quantity of heat required to raise the temperature of unit mass of water by one degree. This heat quantity is designated the calorie in the cgs system and the kilocalorie in the mks system, and in both cases temperature is expressed in degrees Celsius (Centigrade). As the specific heat capacity is a function of temperature, it has been necessary to set a datum temperature which is chosen as 298 K or 25°C. 

Special correlations have also been developed for liquid metals, used in recent years in the nuclear industry with the aim of reducing the volume of fluid in the heat transfer circuits. Such fluids have high thermal conductivities, though in terms of heat capacity per unit volume, liquid sodium, for example, which finds relatively widespread application, has a value of Cpp of only 1275 k.l/ni1 K. 

A flow of I kg/s of an organic liquid of heat capacity 2.0 kJ/kg K is cooled from 350 to 330 K by a stream of water flowing countcrcurrently through a douhle-pipe heat exchanger. Estimate the effectiveness of the unit if the water enters the exchanger at 290 K and leaves at 320 K. 

Heat energy will flow from an object of a high temperature to an object of a lower temperature. An object with a high temperature does not necessarily contain more heat energy than one with a lower temperature as the temperature change per unit of heat energy supplied will depend upon the specific heat capacity of the object in question. 

The SI unit for heat capacity is J-K k Molar heat capacities (Cm) are expressed as the ratio of heat supplied per unit amount of substance resulting in a change in temperature and have SI units of J-K -moC (at either constant volume or pressure). Specific heat capacities (Cy or Cp) are expressed as the ratio of heat supplied per unit mass resulting in a change in temperature (at constant volume or pressure, respectively) and have SI units of J-K -kg . Debye s theory of specific heat capacities applies quantum theory in the evaluation of certain heat capacities. 

For liquid water and for aqueous solutions we wiU assume Cp = 1 cal/g K, and, since the density p of water is -1 g/cm, we have pCp = 1 cal/cm K or pCp =1000 cal/Uter K. To estimate the heat capacity of gases, we will usually assume that the molar heat capacity Cp is j R cal/mole K. There are thus three types of heat capacity, the heat capacity per unit mass Cp, the heat capacity per unit volume pCp, and the heat capacity per mole Cp. However, we will use heat capacity per unit volume for much of the next two chapters, and we use the symbol pCp for most of the equations. 

Be sure that your units of heat, mass, and temperature match those used in your specific heat capacity before attempting any calculations. 

Useful quantitation of heat q as a quantity of energy can be traced to the studies of Joseph Black around 1803. Black recognized that different substances vary in their capacity to absorb heat, and he undertook systematic measurements of the heat capacity C (the ratio of heat absorbed to temperature increase) for many substances. He recognized that a fixed quantity of any pure substance (e.g., 1 g of water) has a unique value of C, which can be chosen as a calorimetric standard for defining quantity of heat in a convenient way. In this manner, he introduced the calorie as a unit of heat ... 

A simplified definition of heat capacity is the amount of energy needed to raise the temperature of a material by 1°. Various units for heat capacity include cal/(g-mole)(°C), kcal/(kg-mole)(°C), Btu/(lb-mole)(°F), cal/(g)(°C) or Btu/(lbm)(°F). Heat capacity curves for water vapor and air are given in Figure 2.2. 

Calorimetric (DSC) measurements yield thermodynamic properties of duplex melting in these oligonucleotides independent of any assumptions concerning the model of melting, such as a cooperative all-or-none process versus a noncooperative, multiple-stage melting process. Comparison of calorimetric enthalpies with van t Hoff enthalpies obtained either from the manipulation of heat capacity curves outlined in equations (16.19) to (16.22), or from optical or NMR measurements [equations (16.14) to (16.17)] allows conclusions to be drawn concerning the size of the cooperative unit. If the two... 

The heat capacity of coal can be measured by standard calorimetric methods that have been developed for other materials (e.g., ASTM C-351). The units for heat capacity are Btu per pound per degree Fahrenheit (Btu/lb-0F) or calories per gram per degree Celsius (cal/g °C), but the specific heat is the ratio of two heat capacities and is therefore dimensionless. 

Thermodynamics of complex formation, discussed in detail by Schmidtchen in the present volume, hold many surprises.[32] In comparing enthalpic with entropic parameters one should not forget that AG and AS depend on the chosen units for relative concentration, which can be either mol/1, or can be given in dimensionless mole fractions in consequence the usual partition of absolute numbers for AH and AS becomes to some degree arbitrary (see e.g. ref. 2d, p. 24, p. 106). In addition, complexation is usually characterized by sizeable changes of heat capacity, making the thermodynamic partitions temperature-dependent. 

The calculation of sensible heat is based on the heat capacity (at constant pressure) of the substance, CP(T), which is in units of heat (energy) per unit mass. Heat capacity information is typically in the form of coefficients for a polynomial expression... 

Remark 7.6. The analysis framework we presented is also applicable if an inert component is used to increase the heat capacity of the reaction mixture. In this case, the model (7.2f) would be augmented by the equations corresponding to the model of the separation unit. However, the stoichiometric matrix S and reaction rates r would remain unchanged, since the inert component does not partake in any reaction. Furthermore, the analysis can be applied if more complex correlations are used for the physical parameters of the system (e.g., temperature dependence of heat capacities and densities), as long as the basic assumptions (7.27), (7.29), and (7.30) apply. 

Figure 3.27 Calculation of heat capacity of an unknown using a Netzsch DSC200 heat-flux DSC [7]. The distinct shift in heat capacity at 690°C corresponds to the glass transition temperature (see section 7.6). A 191 mg sapphire standard was used as calibrant for a 130 mg (laser special) glass sample. All heating ramps were at 20°C/min (faster heating rates permit greater temperature lags). The right hand scale, in the original units of the differential thermocouple, is inverted in exothermic and endothermic directions as compared to the usual convention in this book.

CYCLE TIME FOR MINIMUM COST PER UNIT OF HEAT TRANSFER There are many different circumstances which may affect the minimum cost per unit of heat transferred in an evaporation operation. One simple and commonly occurring case will be considered. It may be assumed that an evaporation unit of fixed capacity is available, and a definite amount of feed and evaporation must be handled each day. The total cost for one cleaning and inventory charge is assumed to be constant no matter how much boiling time is used. The problem is to determine the cycle time which will permit operation at the least total cost. 

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