Definition of Temperature
and Entropy Change upon Heating
of Systems at variing Temperature

We have been stating that at high temperature, adding a given amount of heat to a system, raises its entropy less than does the same amount of heat at a low temperature. This is a statement about how entropy changes upon a change on internal energy, caused by the addidion of heat to a system. The conclusion has been drawn from the consideration of the line in a U versus S diagram that shows how internal energy changes upon change of entropy -- the inverse of what we have been stating. The connection can be seen upon a rotation of the corresponding diagram, as shown below.


Picture 2This correspondence can be seen easily if the diagram is rotated such that the axes are exchanged, as shown.

And this is the result.


Picture 3This is the result of the above operation. I have taken the same image as in picture 1 and rotated it; I left the subscripts out of the operation in order to leave them more readable.

Compare this to the original diagram in the temperature article:


Picture 1The image shows how internal energy changes upon increase of entropy; if this suggests to you that it must be possible to take control of the entropy of a system, then you are on the right path. Keep in mind that the changes in the system we are discussing here are caused by the addition of heat, and this, by definition, is the transfer of energy while changing entropy. Thus, by heating or cooling (among other), you can control the entropy of a system.


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