Heat capacity specific, definition

The partial molar properties are not measured directly per se, but are readily derivable from experimental measurements. For example, the volumes or heat capacities of definite quantities of solution of known composition are measured. These data are then expressed in terms of an intensive quantity—such as the specific volume or heat capacity, or the molar volume or heat capacity—as a function of some composition variable. The problem then arises of determining the partial molar quantity from these functions. The intensive quantity must first be converted to an extensive quantity, then the differentiation must be performed. Two general methods are possible (1) the composition variables may be expressed in terms of the mole numbers before the differentiation and reintroduced after the differentiation or (2) expressions for the partial molar quantities may be obtained in terms of the derivatives of the intensive quantity with respect to the composition variables. In the remainder of this section several examples are given with emphasis on the second method. Multicomponent systems are used throughout the section in order to obtain general relations. 

Specific Heat Capacity. Specific heat capacity is, by definition, the quantity of heat required to raise the temperature of a unit mass of material by one degree. As such, this quantity may be considered a measure of the thermal energy storage capacity of a substance. Specific heat capacity is expressed in SI units as J/(kg-K), in English units as Btu/(lb-°F), and in cgs units as cal/(g °C). 

Definition.—The heat capacity of unit mass of a substance is called its specific lieat. 

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. 

In all of these systems, by definition, the specific heat capacity of water is unity. It may be noted that, by comparing the definitions used in the SI and the mks systems, the kilocalorie is equivalent to 4186.8 J/kg K. This quantity has often been referred to as the mechanical equivalent of heat J. 

The temperature profile of a planetary atmosphere depends both on the composition and some simple thermodynamics. The temperature decreases with altitude at a rate called the lapse rate. As a parcel of air rises, the pressure falls as we have seen, which means that the volume will increase as a result of an adiabatic expansion. The change in enthalpy H coupled with the definition of the specific heat capacity... 

The specific heat capacity commonly has units of J/g-K. Because of the original definition of the calorie, the specific heat capacity of water is 4.184 J/g-K. If the specific heat capacity, the mass, and the change of temperature are all known, the amount of energy absorbed can easily be calculated. 

If the heat capacity of a chemically complex melt can be obtained by a linear summation of the specific heat of the dissolved oxide constituents at all T (i.e., Stebbins-Carmichael model), the melt is by definition ideal. The addition of excess Gibbs free energy terms thus implies that the Stebbins-Carmichael model calculates only the ideal contribution to the Gibbs free energy of mixing. 

The specific and molar heat capacities of some common substances are given in Table 6.1. Note that, although the values of the specific heat capacities are listed in joules per degree Celsius per gram (J-(°C) 1 -g 1), they could equally well be reported in joules per kelvin per gram (J-K 1-g ) with the same numerical values, because the size of the Celsius degree and the kelvin are the same. We can calculate the heat capacity of a substance from its mass and its specific heat capacity by rearranging the definition Cs = dm into C = mCs. Then we can use... 

By definition, the heat capacity of a system is the amount of energy required to raise its temperature by 1 K. The unit is J KT1. To allow calculations and comparisons, the specific heat capacity is more commonly used ... 

These definitions accommodate both molar heat capacities and specific heat capacities (usually called specific heats), depending on whether U and H are molar or specific properties. 

The following symbols are used in the definitions of the dimensionless quantities mass (m), time (t), volume (V area (A density (p), speed (u), length (/), viscosity (rj), pressure (p), acceleration of free fall (p), cubic expansion coefficient (a), temperature (T surface tension (y), speed of sound (c), mean free path (X), frequency (/), thermal diffusivity (a), coefficient of heat transfer (/i), thermal conductivity (/c), specific heat capacity at constant pressure (cp), diffusion coefficient (D), mole fraction (x), mass transfer coefficient (fcd), permeability (p), electric conductivity (k and magnetic flux density ( B) ... 

A temperature change AT from Tj leads to a change AO in specific internal energy. As AT - 0, the ratio AW/AT approaches a limiting value (i.e., the slope of the curve at Ti), which is by definition the heat capacity at constant volume of the substance, denoted by Cv... 

This definition accommodates both the molar heat capacity and the specific heat capacity (usually called specific heat), depending on whether U is the molar or specific internal energy. Although this definition makes no reference to any process, it relates in an especially simple way to a constant-volume process in a closed system, for which Eq. (2.16) may be written ... 

The specific heat of a substance is represented by Cp and is the energy as heat needed to raise the temperature of one gram of substance by one kelvin. Remember that molar heat capacity of a substance, C, has a similar definition except that molar heat capacity is related to moles of a substance not to the mass of a substance. Because the molar mass is the mass of 1 mol of a substance, the following equation is true. 

Section 12.2 defines specific heat capacity as the amount of heat required to increase the temperature of 1 g of material by 1 K. That definition is somewhat imprecise, because, in fact, the amount of heat required depends on whether the process is conducted at constant volume or at constant pressure. This section describes precise methods for measuring the amonnt of energy transferred as heat during a process and for relating this amonnt to the thermodynamic properties of the system under investigation. 

The definition of the specific molar heat capacity of the reference state, Cp, and the determination of the correction factor, CF(Zm, 6), are discussed next. The specific molar heat capacity of the reference state, Cp, is defined by... 

Definition of the specific molar heat capacity of the reference state, Cpg, for gas-phase and liquid-phase reactions... 

Given that (see Fig. 9.8) at the glass transition temperature, the specific volume Vs and entropy S are continuous, whereas the thermal expansivity a and heat capacity Cp are discontinuous, at first glance it is not unreasonable to characterize the transformation occurring at Tg as a second-order phase transformation. After all, recall that, by definition, second-order phase transitions require that the properties that depend on the first derivative of the free energy G such as... 

As we shall see, most authors ascribe this effect to the energies of the initial state and the transition state being influenced by temperature to different extents. In this interpretation, therefore, these reactions exhibit a temperature-dependence of Ea that corresponds to the fundamental definition of a specific heat of activation, given in Section III. A (100). This is in contrast with the nonzero values of dEaldT derived in the previous section. Robertson et al. (142,149) have gone so far as to call them spurious heat capacities, whereas the effects we are dealing with in this section are termed real heat capacities. 

The fact that we have not addressed all the different types of heat capacities became evident at the end of the subsection on "Neat content" where a certain difficulty became apparent in our two prototypical example systems. Along with the integral quantities dealt with above, we need various specific (related to the mass) and molar (related to the amount of substance) quantities derived from them. We can omit them here because their definitions and applications follow known patterns. 

Solution No. Equation fq-ial applies to a specific path (constant-volume for Cv, constant-pressure for Cp). Once the path is specified, the amount of heat that is exchanged (jdQ) is uniquely defined and depends on the local state of the system. It is best to view eqs. and (t-iSi as the definitions of the heat capacities because they make clear that both Cv and Cp are state functions. 

V and can be derived from the definition of the heat capacity dQ/dT = mCp. The symbols have the standard meanings p is the density and Cp, the specific heat capacity per unit mass, so that m = Vp. 

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