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I hope I was clear here. I just want to know if my understanding of temperature is correct, and what the concept of temperature means in the world of quantum physics? WHAT is temperature, as scientists understand it today?

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- Thread starter student85
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I hope I was clear here. I just want to know if my understanding of temperature is correct, and what the concept of temperature means in the world of quantum physics? WHAT is temperature, as scientists understand it today?

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malawi_glenn

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Thanks for your responses guys, that helped.

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Fredrik

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It isn't. It's a measure of how much the energy changes when you change the entropy of the system, or equivalently 1 divided by how much the entropy changes when you change the energy. It's usually defined by taking entropy S to be a function of energy E and defining the temperature T(E)=1/S'(E).From a classical point of view I believe temperature is a measure of the internal energy of an object,

The point of the concept of temperature is that it tells you in which direction energy will flow when you put two systems in thermal contact. If the total energy of the two systems is constant (it will be unless they interact with a third system), energy will flow from the system with the higher temperature to the one with the lower temperature. It's actually not very difficult to show that this must happen if the combined system goes towards a state of higher entropy.

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Fredrik

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Consider two systems that are put in thermal contact with each other. If we keep them isolated from other systems, the total energy is [itex]E=E_1+E_2[/itex] and the total entropy is [itex]S(E)=S(E_1)+S(E_2)[/itex]. Energy will flow from one system to the other if that increases the total entropy of the combined system. Let's say that the total entropy increases when energy flows from system 1 to system 2. That means that

[tex]0<\frac{d}{dE_2}(S_1(E-E_2)+S_2(E_2))=-S_1'(E_1)+S_2'(E_2)[/tex]

[tex]\frac{1}{S_1'(E_1)}>\frac{1}{S_2'(E_2)}[/tex]

This shows that the energy flows from the system with the higher value of [itex]1/S_i'(E_i)[/itex] to the one with the lower value. We therefore define the

[tex]T(E)=\frac{1}{S'(E)}[/tex]

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