Quote by CraigH
This confuses me, surely as the heat added increases ( dQ), then the temperature will also increase, so it should be (dT)
Unless T is a different constant for each example?

It is dS = dQ/T.
Why am I so confident I am right?
Well lets note some important facts. As temperature approaches infinity, entropy S is at a maximum. The way to increase temperature is to add heat Q. So maybe entropy S is a function of Q.
lets differentiate S. dS/dQ. To maximize S, dS/dQ = 0. This is exactly true when temperature is infinite for the expression dS/dQ = 1/T. Makes sense?
But wait, you say. Maybe entropy is actually a minimum at T > ∞. No that's silly, because you can check the 2nd derivative. d/dQ (dS/dQ) = d/dQ (1/T) = 1/T^2. When the first derivative is zero and the second derivative is negative at a point, the maximum is described.
Therefore dS/dQ = 1/T is a correct formula, give or take some coefficients, perhaps like the Boltzmann constant. Redistribute it. dS = dQ/T.