Heat capacity symbol

Figure 1 Experimental heat capacities (symbols) compared with calculated values (lines) of carbon dioxide (a) and argon (b), respectively...

For pure substances, the heat capacity is often expressed per mole or per gram of substance. The molar heat capacity at constant pressure (symbol j ) is the quantity of heat required to raise the temperature of one mole of a substance by one degree under the condition of constant pressure. The constant-pressure specific heat capacity (symbol, Cp), sometimes called the specific heat is the quantity of heat required to change the temperature of one gram of a substance by one degree at constant pressure. Here are the values for water at 25 °C. 

The brackets symbolize fiinction of, not multiplication.) Smce there are only two parameters, and a, in this expression, the homogeneity assumption means that all four exponents a, p, y and S must be fiinctions of these two hence the inequalities in section A2.5.4.5(e) must be equalities. Equations for the various other thennodynamic quantities, in particular the singidar part of the heat capacity Cy and the isothemial compressibility Kp may be derived from this equation for p. The behaviour of these quantities as tire critical point is approached can be satisfied only if... 

Name of gas Chemical formula or symbol Approx. molecular weight, M Weight density (lb/ft3) Specific gravity relative to air, So Individual gas constant, R Specific heat at room temperature [Btu/(lb °F)] Heat capacity per cubic foot k equal to cp/cv... 

Gas Chemical formula or symbol Approximate molecular weight (M) Heat capacity ratio 7 = CpICy... 

Figure 8.2 Molar heat capacity at constant pressure of H(g), H2(g) and H20(g). The open symbols at 5000 K represent the limiting classical heat capacity.

The symbol 9 is called the characteristic temperamre and can be calculated from an experimental determination of the heat capacity at a low temperature. This equation has been very useful in the extrapolation of measured heat capacities [16] down to OK, particularly in connection with calculations of entropies from the third law of thermodynamics (see Chapter 11). Strictly speaking, the Debye equation was derived only for an isotropic elementary substance nevertheless, it is applicable to most compounds, particularly in the region close to absolute zero [17]. 

Figure 5.56 Maier-Kelley heat capacity functions for various structural forms of the KAlSi30g (A) and NaAlSi30g (B) feldspar end-members (solid curves), compared with T derivative of hnite differences at various T (hlled symbols) (from Helgeson et ah,...

Cp - Cy equals [P + (dU/dV)T](dV/dT)p. The dUldV term is often referred to as the internal pressure and is large for liquids and solids (See Internal Pressure). Since ideal gases do not have internal pressure, Cp - Cy = nP for ideal gases. The ratio of the heat capacities, Cp/Cy, is commonly symbolized by y. 

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. 

The quantities C and H are extensive, meaning that they are proportional to the amount of material involved in the process or reaction. We choose to let c, cp, and cv represent specific heat capacities with the lower case symbol, w, for the sample s mass. Then,... 

Fig. 7. The excess heat capacity of DyF3 curve shows the values calculated from the crystal field energies, symbols are tiie values derived from the experimental data by subtracting Qat, as explained in tiie text.

Fig. 15 Low-temperature molar specific heat of tetragonal filled triangles), orthorhombic (dots), and depolymerized C60 (open symbols), plotted as Cp/T3. Reprinted with permission from A Inaba, T Matsuo, A Fransson, and B Sundqvist, Lattice vibrations and thermodynamic stability of polymerized C60 deduced from heat capacities , J. Chem. Phys. vol. 110 (1999) 12226-32 [105]. Copyright 1999 American Institute of Physics...

Let symbols without subscripts refer to the solid and symbols with subscript w refer to the water. Heat transfer from the solid to the water is manifested by changes in internal energy. Since energy is conserved, AU = —At/, . If total heat capacity of the solid is C (= mC) and total heat capacity of the water is C w (= mwCw), then ... 

In this equation H = pcAh is the heat capacity of the element where c is the specific heat of the pyroelectric material and, in this context, p is its density. In what follows the product pc, the volume specific heat, is given the symbol c. ... 

Property values in the standard state are denoted by the degree symbol (°). For example, C°P is the standard-state heat capacity. Since the standard state for gases is the ideal-gas state, C% for gases is identical with Cj , and the data of Table 4.1 apply to the standard state for gases. All conditions for a standard state are fixed except temperature, which is always the temperature of the system. Standard-state properties are therefore functions of temperature only. 

A substance with a large specific heat capacity can absorb and release more energy than a substance with a smaller specific heat capacity. The symbol that is used for specific heat capacity is a lower-case c. The units are J/g-°C. 

Heat capacity is symbolized by an upper-case C. It is usually expressed in the unit J/°C. 

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) ... 

In (1.18.12) the symbols Cv and CP represent the heat capacities at constant volume and constant pressure, respectively. As will be seen in Section 1.19, these quantities represent the heat absorbed by a system per unit increase in its temperature under the indicated constraints. Such a quantity may be measured experimentally by use of a calorimeter. Equations (1.18.12) thus furnish a basis for determining E, H, or S from experimental measurements. 

Fig. 4. The apparent specific heat capacity of lysozyme from 0 to 0.45 g of water per gram of protein. The curve is calculated. The heat capacity measurements were made with lyophilized powders of lysozyme, appropriately hydrated, except for the four measurements indicated by the square symbols, for which the sample was a film formed by slowly drying a concentrated solution of lysozyme. From Yang and Rupley (1979).

Heats of reaction at any temperature can be calculated from heat-capacity data if the value for one temperature is known the tabulation of data can therefore be reduced to the compilation of standard heats of formation at a single temperature. The usual choice for tlris temperature is 298.15 K or 25°C. The standard heat of fomration of a compound at tlris temperature is represented by the symbol AHJ. The degree symbol indicates tliat it is the standard value, subscript / shows that it is a heat of fomration, and the 298 is the approximate absolute temperature in kelvins. Tables of these values for common substances may be found in standard handbooks, but the most extensive compilations available are in specialized reference worlai. An abridged list of values is given in Table C.4 of App. C. 

The molar heat capacity of a pure substance is the energy as heat needed to increase the temperature of 1 mol of the substance by 1 K. Molar heat capacity has the symbol C and the unit J/K mol. Molar heat capacity is accurately measured only if no other process, such as a chemical reaction, occurs. 

By definition dU/dT)v is the heat capacity at constant volume, given the special symbol C. For most practical purposes in this text the term (dU/BV)r is so small that the second term on the ri t-hand side of Eq. (4.4) can be neglected. Consequently, changes in the internal energy can be computed by integrating Eq. (4.4) as follows ... 

---