Assume there is a function of systems at equilibrium, which gives it's heat energy. So if X is a certain amount of substance in a certain equilibrium state, we have: E(X) as the total heat energy.

Obviously E(nX) = nE(X) where n is a multiplier -- or the total

Now the defining property of heat flow is it always flows from hot to cold. So if there is no heat flow, the systems must have the same temperature. This is the Zeroth Law.

Even though E(2X) > E(X), both 2X and X must be at the same temperature. T(nX) = T(X)

Now lets take two different items at different temperatures and put them in contact. E(X) and E(Y).

After a time, heat flow trickles to a stop and X reaches a new equilibrium state at a new temperature. X->X'. Likewise, Y->Y'. And the temperatures are the same. T(X') = T(Y'). But why that particular temperature?

For that, we need the Second Law of Thermodynamics, the one about entropy. Like energy, the amount of entropy of a substance in a particular state is proportional to the amount of the substance. So S(nX) = nS(X)

So T(X') = T(Y') because if significant amounts of energy would to flow from X' to Y' (or vice versa) the total entropy would decrease. So at this equilibrium temperature T(X') = T(Y') = t, only infinitesimal amounts of of energy can be exchanged, with no change of entropy. So a tiny change in the energy of X', ∂E(X') can flow to Y' and cause the oppose tiny change in engery, -∂E(Y'), only if the change in entropy is also equal and opposite, ∂S(X') = -∂S(Y').

So at a certain temperature, t, equal and opposite tiny changes to E produce equal and opposite changes in S.

So it follows, at this particular temperature, t, that ∂S(X')/∂E(X') = ∂S(Y')/∂E(Y'), and since this has to be true for any two substances, then ∂S(X')/∂E(X') = f(t). From just the zeroth law and the second law, we can't say what this function of temperature is f(t) is, but it has to be the same for all substances.

But we have no obvious meters that read S. And no meters, therefore that read ∂S or f(t). So it is up to physicists to make the world not only predictable, but simply predictable. So we will define the definitions in a way that makes the math simplest as possible.

By definition, ∂S(X)/∂E(X) = 1/T(X) -- and you can see this is hinted by the units. S is measured in Joules per Kelvin, and E in Joules.

Combining this with the First Law, we get ∂E(X) = T(X)∂S(X) - Work, which is just a a restatement of conservation of energy. For a gas, work might be Pressure × ∂Volume.

understood ... The tail end left me with a little doubt but achievable by potential possibly. Na the last part looks like speculation but a lot of that is true . I got it

Mekigal

6th June 2013 - 10:11 PM

QUOTE (Chaman+May 14 2013, 10:06 AM)

There is a fundamental difference between temperature and heat. Heat is the amount of energy in a system. The SI units for heat are Joules. A Joule is a Newton times a meter. A Newton is a kilogram-meter per second squared. Heat is transferred through radiation, conduction and convection. The amount that molecules are vibrating, rotating or moving is a direct function of the heat content. Energy is transported by conduction as molecules vibrate.

Yeah I am with you. Like pressure and volume . There are different states of heat You got radiant heat and forced motion heat in atmospheres . We say forced air where the air is heated and has lost capability of radiation to another object . Then Radiant heat don't heat the air it heats the object it strikes

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