Cloudscape

Below we come to a number of formulae which relate dimensionless heat capacity to heat in a striking way, showing, notably, that pressure times volume is a constant fraction of heat. The formula of specific heat capacity is c = Q/mT According to the ideal gas law, Q = NkT on a microscopic level, so that c = Nk/m = k/M (where M is mass per molecule). Q = cmT Now, according to the ideal gas law, PV = nRT ⇔ T = PV/nR If we substitute this, we get: Q = cmPV/nR As m = nM, Q = cMPV/R ⇔ PV = Q · (R/cM) Now, heat capacity is the ability of a substance to store heat with increase of temperature. It is equal to the product of mass and specific heat capacity (the heated needed to heat a kilogram of a substance by one kelvin): C = cm, and, according to the heat equation, Q = cmT, so that this is equal to C = Q/T Now, the dimensionless heat capacity of a substance is equal to its heat capacity divided by the number of moles times the universal gas constant: C* = C/nR, the inverse of which is: 1/C* =nR/C Now, the number of moles equals the total mass divided by the mass of one mole. Substituting m/M in n, we get: 1/C* =mR/MC, and, as said, C = cm, so that 1/C* = R/cM. Substituting this in the formula we got earlier, ideally: PV = Q · (R/cM) we get: PV = Q/C*, This formula may be useful because it relates heat, pressure and volume, showing that pressure times volume is a constant fraction of heat. Now, according to kinetic theory, P = ⅓ρv^2 ⇔ PV = ⅓mv^2 ⇔ PV = ⅔Ek Thus, ⅔C*Ek = Q This formula succinctly relates heat to kinetic energy. Note that kinetic energy equals work divided by two, so that ⅓C*W = Q Also, according to the Dulong-Petit law, any crystal has a dimensionless heat capacity of 3, so that 2Ek = Q ⇔ W = Q This means that, for any crystal, the heat of a crystal is the total work it may perform. This means that its internal energy twice its heat: U = W+Q = 2Q = 2W

On the influence of the distribution of charges on the total strength of the forces mediated between them: Distributivity.rtf This is of immense importance to the cohesion of all matter. The formula included may be useful someday in foglet technology because foglets would adhere to one another through magnetism, to calculate the required charge to keep their total mass together with a specified strength.

If either the age, size, energy or complexity of the universe are infinite, so are the others: if the universe is infinite in age, it must be infinite in size because a finite universe would keep expanding, ergo in energy, because it would otherwise be of infinitely low density due to this expansion, ergo in complexity because this energy would be distributed amongst the universe rather than remaining infinitely accumulated. If the universe is infinite in size, it must be infinite in age because if it had a starting point it would originate from a singularity rather than popping into existence in infinite dimensions, and infinite in energy and complexity because it would otherwise be of infinitely low density as formerly said. If the universe is infinite in energy, it must be infinite in age because in order to become of finite density it'd otherwise have to expand with infinite speed (this is the most plausible other possibility, as the absolute speed of light might not be absolute), infinite in size for the same reason, and infinite in complexity because of its infinite size. Infinite complexity basically equals infinite size because size is relative. If the universe is infinite up or down, it makes little difference. Suppose the universe was contained inside a giant atom (which would have an infinitely complex substructure, so that this would be possible!), we'd still say the universe is tens of billions of light years in diameter instead of one and a half femtometer. Relative to an infinitely small world (at an infinitely complex level), everything is infinitely large. As we've said, infinite size and finite density means infinite energy. However, if the universe is infinite in complexity this does not necessarily mean that it is infinite in age. Thus, we conclude that either: 1) the age, size, energy and complexity of the universe are all infinite, 2) neither the age, size, energy or complexity of the universe are infinite 3) the size, energy and complexity, but not the age, of the universe are infinite, and the Theory of Relativity is incomplete. You can scratch the latter two possibilities, however, if you can accept the following argument. Existence cannot have had an actual cause, because that cause would itself have to be part of existence, otherwise it could not have existed because it would then not be part of existence. Why would there be a beginning? Where did it come from? What caused it? Now, I'm talking about the whole of existence, not just our own reality, but any reality at all, including hypothetical realities in which our own universe was created. Unless there already existed "something" which had caused the universe to arise, ie there was already something in *existence* (in other words, in the universe), such cause would necessarily have been acausal, and for something to be science it must obey causality. Causality, then, is its own only exception. Everything has a cause, but the chain of causes and consequences itself hasn't. Following this line of reasoning we conclude that the universe is infinite in age, size, energy and complexity.