Paradoxical cooling

There is an apparent paradox here that as the cooled cycle contains an irreversible process (constant pressure mixing), its efficiency might be expected to be lower than the original uncooled cycle. The answer to this paradox follows from consideration of all the irreversibilities in the cycle and we refer back to the analysis of Section 3.2.1.1, for the rational efficiency of the [CHT]ru cycle. The irreversibility associated with the heat supply is unchanged, as given in Eq. (3.3), but the irreversibility associated with the heat rejection between temperatures T(, and T) = Ta becomes... 

This type of cake is often stored for a while after baking because it is to be covered with royal icing. The cake not only needs to cool but the surface needs to equilibrate with the bulk. There is a paradox that if the cake is just wrapped in greaseproof paper and kept in a tin that is not air tight there will be no problem. However, if the cake is wrapped in aluminium foil and kept in an air tight tin there is a possibility of mould formation because with the better moisture barrier any condensation or sweating can not evaporate. 

Let us now turn to a discussion of the relation of the temperature dependence of the polymer melt s configurational entropy with its glass transition and address the famous paradox of the Kauzmann temperature of glass-forming systems.90 It had been found experimentally that the excess entropy of super-cooled liquids, compared with the crystalline state, seemed... 

Some forty-eight years from the time the BCS theory was proposed, a large number of experimental evidence on superconductivity has accumulated. But, they do not seem to support the theory. Some obvious paradox is experimentally, the higher the resistivity at room temperature, the more likely that metal will be a superconductor when cooled. This directly contradicts the BCS s idea that paired electrons originate from fermi electrons. Further, if paired electrons (boson) indeed come from fermi electrons... 

One paradox in all this troubled mankind greatly until about the time of the outbreak of World War II. If heat energy leaks from an object, it cools. Children learn... 

The limit Pe 0 yields the pure conduction heat transfer case. However, for a fluid in motion, we find that the pure conduction limit is not a uniformly valid first approximation to the heat transfer process for Pe 1, but breaks down far from a heated or cooled body in a flow. We discuss this in the context of the Whitehead paradox for heat transfer from a sphere in a uniform flow and then show how the problem of forced convection heat transfer from a body in a flow can be understood in the context of a singular-perturbation analysis. This leads to an estimate for the first correction to the Nusselt number for small but finite Pe - this is the first small effect of convection on the correlation between Nu and Pe for a heated (or cooled) sphere in a uniform flow. 

Interestingly enough, if a glass-forming liquid were cooled slowly enough (at several times the age of the universe ) such that it follows the dotted line shown in Fig. 9.8Z) at a temperature T kau the entropy of the supercooled liquid would become lower than that of the crystal — a clearly untenable situation first pointed out by Kauzmann and referred to since as the Kauzmann paradox. This paradox is discussed in greater detail in Sec. 9.4.2. 

In equation 2 Tr denotes the freezing temperature at an infinitely slow cooling rate. For this limit the abbrevation Tr was chosen to remind of the Kauzmann paradox (6,33), which originates from a similar extrapolation procedure. Tr will... 

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