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Sounds like it's the same thing.

They are closely related but not the same. DeltaS = DeltaQ /T

A lot of it comes down to whether a process is reversible or not. I've taken multiple courses on thermodynamics and still only understand it a little.

It is not. Two bodies can have different entropy even if they are emitting the same amount of heat.

Where are the calculations?

dS = dQ / T

So T = dQ/dS. Seems like the same thing.

If they were the same thing, then T=1. Since there are many many bodies with T != 1, it follows that dQ is rarely equal to dS.

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