Specific heat temperature polynomial

The specific heat of the fluid is treated as the polynomial function of temperature, while the thermal conductivity of the fluid and solid and the specific heat of the solid part are assumed to be independent of the temperature. 

The heat capacity increases with temperature, for example, for liquid water at 20 °C the specific heat capacity is 4.182 kj kg 1 K 1 and at 100 C is 4.216k kg 1K 1 [2]. Its variation is frequently described by the polynomial expression (virial equation) ... 

First, second and 5th order polynomial interpolation for the specific heat capacity of a semi-crystalline thermoplastic (PA6). When performing a heat transfer simulation (heating or cooling) for a thermoplastic, the complete course of the specific heat capacity as a function of temperature is needed. A common way to do this... 

A first, second and 5th order polynomial interpolation will be performed in order to obtain the specific heat for three different temperatures. 

The results for each interpolation are shown in Table 7.2 and Fig. 7.4 For 190°C and 250°C, the specific heat is locally a smooth function, therefore the three different schemes give very accurate results. The problem is for the 220°C, this temperature is right in the middle of the melting. The linear interpolation can use only two points, whereas the 2nd and 5th interpolation use more points following the behavior closer. For this particular case the 5th order interpolation is the one that mimics best the complete curve obtained from the equation. However, as already mentioned, we must be careful because a polynomial interpolation of a very high order can lead to oscillations [19]. 

The specific heats, Cp are usually expressed as a quadratic or a polynomial function of temperature and expressed as ... 

The above-mentioned method was initially developed for measuring the isobaric heat capacities of aqueous salt solutions up to 573 K and 30 MPa. For a typical run, the sample cell was loaded with the sample solution and the reference cell was loaded with a reference fluid of known heat capacity (usually water). Then, the temperature was increased from to T, at constant pressure, and the difference Q in the transferred heat was corrected taking into account both the cell s volumetric dissymmetry and the differences between the densities and specific heat capacities of the measured sample and reference fluids, respectively. Such an experiment allows the measurement of the product pCp representing the isobaric heat capacity divided by volume. In order to obtain the desired isobaric heat capacity, Cp, of the solution, it was necessary to know its density. For this purpose, the isobaric specific heat capacity and density were represented by polynomials in terms of temperature T ... 

The parameters for the density polynomial were obtained from available corresponding densities. Knowing the calibration constant for each set of experiments and the densities of the measured fluids allowed the calculation of c, and finally the specific heat capacity. The performances of the calorimetric arrangement have been tested by measuring the heat capacity for liquid n-hexadecane as well as of NaCl (aquous) in the molality range 0.1-2.0 mol kg". Measurements taken at different temperatures and pressures compare well with the literature data.. ... 

Specific heat is another term used when heat capacity is expressed on a per mass basis. Heat capacities are a function of temperature and are usually expressed as a polynomial such as... 

The molal specific heat of gases is conventionally given as a polynomial in temperature. 

In this problem, we compare the temperature dependence of the specific heat of triatomic ideal gases based on statistical thermodynamics and classical/empirical polynomials. Locate the appropriate molecular data for carbon dioxide (CO2) and nitrogen dioxide (NO2) that will allow you to compute and graph the specific heat at constant pressure Cp for both gases from 300 to 800 K at atmospheric pressure. The graphs that are generated should be based on calculations from statistical thermodynamics. 

Locate the appropriate coefficients that describe empirically the temperature dependence of the specific heat for both carbon dioxide and nitrogen dioxide. The polynomial expression can be written generically in the following form ... 

The relationships between response variables, y, and factors, x, are represented through mathematical expressions that take the form of correlations or regression equations. These linear or nonlinear mathematical expressions are often expressed as a polynomial, logarithmic, exponential, or trigonometric function. For example, the variation of the specific heats of gases, Cp, has been expressed as a third-order polynomial with respect to temperature ... 

The minimum number of experiments that should be conducted is at least equal to the number of parameters in the model. A linear model has two parameters, /3o and (Strictly speaking, y = /Sixi is a linear model and y = Po+Pixi is nonlinear but this nuance will be disregarded in our discussion.) A quadratic model has three parameters (/3o,/3i, and P2) while there are four parameters in a cubic expression (see the relationship between specific heat and temperature above). The number of parameters for a simple polynomial is at most equal to m + 1, where m represents the order of the polynomial. 

The specific heat data in both the low- and intermediate-temperature regimes were analyzed statistically. The low-temperature results were fitted to polynomials in T, which in turn permitted calculation of specific heats at a set of arbitrarily chosen temperatures. 

The lattice specific heats of solids at low temperatures are generally proportional to T. With metals, an electronic term, proportional to T, must also be taken into consideration. For a first approximation, the low-temperature specific heats of normal metals follow the two-term function of (2). In statistical analyses of experimental data, however, improvements in fit have often been obtained by extending that function as a Taylor expansion in odd powers of T, For example, Martin et al [ ] fitted the specific heat of high-purity Cu in the temperature range 0.3 to 30 K to a polynomial of the form Generally, such a procedure... 

Dependence of specific heat on temperature for vapor phase— polynomial form ... 

The specific heat of dry solid Cg is usually presented as a polynomial dependence of temperature. 

The enthalpy of the reaction varies with temperature and depends on the specific heat of each component. For ideal gases, the specific heat varies according to a polynomial function, namely ... 

Usually, the molar and specific heat capacities or pure substances and compounds vary with temperature, and the molar heat capacity is usually provided by the polynomial equation ... 

Specific heat capacity is the amount of heat required to raise the temperature of 1kg of a substance by 1°K. In general form, dq = cdf, where c = specific heat capacity. Specific heat capacity is dependent on temperature. It is useful to express it as a polynomial with respect to temperature. 

At low buffer coucentration tlu heat cairacity of the buffer is not very different from the heat capacity of water. Therefore often the heat capacity of water at room temperature (1 cal/gK = 4.184 J/gK) is used as an approximate value for the specific heat capacity of the buffer Cpj, ir,.,. However, if accurate data are needed, a third measurement of water against Imffer must be performed, which yields the difference in heat capacity between Imffer and water. Since the heat capacity of water is known accurately and can be expressed by the following polynomial equation based on the data of Stimson [4]... 

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