Heat capacity, definitions

Hamiltonian operator, 140 Heat capacity, definition of, 40 Heisenberg uncertainty principle, 124,148 Hermite polynomials, 79 Hermitian operators, 140 Heterogeneous logarithms, 26 Homogeneous logarithms, 26... 

This definition is in terms of a pool of liquid of depth h, where z is distance normal to the surface and ti and k are the liquid viscosity and thermal diffusivity, respectively [58]. (Thermal diffusivity is defined as the coefficient of thermal conductivity divided by density and by heat capacity per unit mass.) The critical Ma value for a system to show Marangoni instability is around 50-100. 

For a simple A B reaction, suppose that the heat capacity Cp of A is larger than the heat capacity for B. The enthalpy of A rises more steeply with temperature increase than that of B hy the definition of heat capacity... 

The remaining question is how we got from G3MP2 (OK) = —117.672791 to G3MP2 Enthalpy = —117.667683. This is not a textbook of classical thermodynamics (see Klotz and Rosenberg, 2000) or statistical themiodynamics (see McQuarrie, 1997 or Maczek, 1998), so we shall use a few equations from these fields opportunistically, without explanation. The definition of heat capacity of an ideal gas... 

By definition, equation 90 is the heat capacity at constant volume ... 

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). 

The most satisfactory calciilational procedure for thermodynamic properties of gases and vapors requires PVT data and ideal gas heat capacities. The primary equations are based on the concept of the ideal gas state and the definitions of residual enthalpy anci residual entropy ... 

Definition.—The heat capacity of a body, under specified conditions, is measured by the number of heat units which must pass into that body to raise its temperature 1° C. 

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

The definition of the extent of mesophase and the evaluation of its radius r, is again based on the thermodynamic principle, introduced by Lipatov 11), and on measurements of the heat-capacity jumps AC and ACf, of the matrix material (AC ) and the fiber-composites (ACP) with different fiber-volume contents. These jumps appear at the glass-transition temperatures Tgc of the composites and they are intimately related, as it has been explained with particulates, to the volume fraction of the mesophase. 

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. 

As explained in Section 6.5, the heat capacity of a substance is the constant of proportionality between the heat supplied to a substance and the temperature rise that results (q = CAT). However, the rise in temperature and therefore the heat capacity depend on the conditions under which the heating takes place because, at constant pressure, some of the heat is used to do expansion work rather than to raise the temperature of the system. We need to refine our definition of heat capacity. 

The constant-volume and constant-pressure heat capacities of a solid substance are similar the same is true of a liquid but not of a gas. We can use the definition of enthalpy and the ideal gas law to find a simple quantitative relation between CP and Cv for an ideal gas. 

From this definition, we can obtain an expression for the temperature dependence of AH of a reaction, if the heat capacity at constant pressure is known. For the pressure dependence, the following fundamental relationship offers a good start ... 

The expression for heat capacity brings out the fact that it is an indefinite quantity even when mass is specified, since 8q is so. This is no longer the case when certain conditions, particularly constant volume or constant pressure conditions, are specified. The heat capacity then becomes a definite quantity as a consequence of 8q becoming a definite quantity. 

Figure 7.17 (a) Magnetic properties of [LaTb] and [Tb2] in the form of yT versus T plot per mole of Tb(lll). (b) Schematic representation of the qubit definition, weak coupling and asymmetry, as derived from magnetic and heat capacity data. 

Fundamental definitions for the two primary magnetic heat capacities may be derived [3] and are ... 

In the methods reported above, the temperature change AT used to measure the heat capacity C(T) was supposed to be so small that the time constant r = R C could considered constant in the AT interval. Let us consider, for example, the thermal discharge of a system with heat capacity C(T) a T and thermal conductance to the bath G(T) a T3 (e.g. a metal sample and a contact resistance to the bath at rB). A AT/TB = 10% gives a At/t = 20% over the interval AT, that is a time constant definitely not constant. 

Nevertheless the heat capacity of a carbon resistor was not so low as that of crystalline materials used later. More important, carbon resistors had an excess noise which limited the bolometer performance. In 1961, Low [61] proposed a bolometer which used a heavily doped Ge thermometer with much improved characteristics. This type of bolometer was rapidly applied to infrared astronomy as well also to laboratory spectroscopy. A further step in the development of bolometers came with improvements in the absorber. In the early superconducting bolometer built by Andrews et al. (1942) [62], the absorber was a blackened metal foil glued to the 7A thermometer. Low s original bolometer [61] was coated with black paint and Coron et al. [63] used a metal foil as substrate for the black-painted absorber. A definite improvement is due to J. Clarke, G. I. Hoffer, P. L. Richards [64] who used a thin low heat capacity dielectric substrate for the metal foil and used a bismuth film absorber instead of the black paint. 

The next step was the introduction of ion implantation to dope Si for thermometers. Downey et al. [66] used micromachining to realize a Si bolometer with an implanted thermometer. This bolometer had very little low-frequency noise. The use of thermometers doped by neutron transmutation instead of melt doping is described by Lange et al. [67], The evolution of bolometers sees the replacement of the nylon wires to make the conductance to the bath, used by Lange et al. with a micromachined silicon nitride membrane with a definite reduction in the heat capacity associated to the conductance G [68],... 

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... 

In the definition of the Prandtl number, Cp is the heat capacity of the gas at constant pressure. 

Starting with the definition of heat capacity in Equation (3.20) ... 

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. 

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