Infinite heat capacity

If a solid is heated at a constant rate and its temperature monitored during the process, the melting curve as illustrated in Fig. 4.1 is obtained. Below the melting point, the added heat merely increases the temperature of the material in a manner defined by the heat capacity of the solid. At the melting point, all heat introduced into the system is used to convert the solid phase into the liquid phase, and therefore no increase in system temperature can take place as long as solid and liquid remain in equilibrium with each other. At the equilibrium condition, the system effectively exhibits an infinite heat capacity. Once all solid is converted to liquid, the temperature of the system again increases, but now in a manner determined by the heat capacity of the liquid phase. 

Review Problems 7.4 Curzon and Ahiborn Cycle with Infinite Heat Capacity Heat Source and Sink... 

The possibility of a zero denominator and an infinite heat capacity can readily be seen in the special case that = / 34 = 0. This occurs when... 

In the discussion of the associated model for the A-C binary, the possibility of an infinite heat capacity at 50 at. % was discussed in connection with Eq. (106). This was shown to arise because the temperature derivative of the mole fraction of the molecular ac species becomes infinite for certain values of the interaction coefficients. This behavior is discussed here only for a simplified version of the model in which the interaction coefficients / 14 and of Eq. (68) for AGJ, are equal and opposite. (These parameters then cancel out of k4 at x = ). The discussion below therefore covers the version of the model applied to Ga-In-Sb. 

Fig. 34. flj is the value of the interaction coefficient evaluated at the melting point of AC(s), TAC. z is a selected value for the mole fraction of the molecular species ac at TAC and equal atom fractions of the components of the binary A-C system. Values of CI%/RTac and z that fall under the upper curve are associated with two other values of z that also satisfy Eq. (A19) for species equilibrium. Values of QJ/RTAC and z falling on the inner curve give an infinite heat capacity. 

The infinite heat capacity at the critical point looks unusual, but this is true of all pure substances. This has been observed experimentally and can be demonstrated using the principles of classical thermodynamics. However, even though the heat capacity is infinite, the enthalpy at the critical point is finite. 

At a phase transition the heat capacity will often show a characteristic dependence upon the temperature (a first-order phase transition is characterised by an infinite heat capacity at the transition but in a second-order phase transition the heat capacity changes discontinuously) Monitoring the heat capacity as a function of temperature may therefore enable phase transitions to be detected. Calculations of the heat capacity can also be compared with experimental results and so be used to check the energy model or the simulation protocol. 

A further physical argument suggests that the Q-motion actually decreases to zero. This follows since the g-system consists of an infinite (continuum) number of degrees of freedom. An initial energy content in the Q-motion must eventually be distributed uniformly among all of the degrees of freedom (equipartition). Effectively, the complete system has an infinite heat capacity, and equilibrium must leave the system at zero temperature. 

Since this case corresponds to a system with infinite heat capacity, it is to be expected that the temperature will be unaffected by changes in reactivity (i.e., power level). However, under these circumstances the negative temperature coefficient cannot be of aid in stabilizing the system and one would expect the power level to rise without limit. Since the result given above reaches a finite value it is clear that this elementary model breaks down when applied to this case however, note that for short times after the addition of 5/co (i.e., fit/hh <3C 1) the power function has the correct form. In this case... 

We follow a path for this transport process analogous to diffusion and chemical reaction. Consider a simple schematic of an apparatus consisting of two heat reservoirs, each of infinite heat capacity, one at temperature T and the other at T2, with Ti > T2, Fig. 8.2. 

Canonical Ensemble In the canonical ensemble, all states have fixed V (volume) and N (the number of molecules), but the energy E fluctuates. The ensemble could be considered as a closed system in contact with a heat bath that has infinite heat capacity. 

The metal matrix of a regenerator undergoes a cyclic variation in temperature because of its less than infinite heat capacity. Fortunately, however, the temperature excursion of the extreme ends of the matrix is much less than that of the central portion, a fact which minimizes the effect of this temperature variation upon thermodynamic efficiency. At very low temperatures the heat capacity of all metals falls to a negligibly small value and it becomes impractical to utilize thermal regenerators. Regenerators constructed of lead have been found to be useful at temperatures as low as 14°K. 

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