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Does the entropy of a system depends on the system's temperature?

I know that $\Delta S_{ext}=\frac{q_{rev}}{T}$ ($q_{rev}$ is the heat in a transformation if it is reversible).

My textbook says that the entropy of the exterior always depends on that formula (so it depends on the temperature).

But it says the entropy doesn't always depends on the formula, and we can only say the that in a transformation the entropy of a system can increase or decrease. So does it depend on the temperature?

Thanks!

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    $\begingroup$ Yes, entropy can depend on temperature (and often does). Examples include things like point defect populations in solids giving rise to configurational entropy, or molecule dissociation in the gas phase. $\endgroup$ – Jon Custer May 10 '16 at 16:45
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Entropy is a physical property of a material that, for a single phase substance of constant composition, can be expressed as a function of temperature and one other intensive physical property such as pressure or specific volume. The equation that you wrote down is a relationship that we can use to determine the change in entropy of a substance from one thermodynamic equilibrium state to another, by devising a reversible process from the first state to the second state, and calculating the value of the integral of dq/T for that process. All reversible processes between these same two states will give exactly the same value for the integral.

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