# Entropy Equatio for a closed system

## Main Question or Discussion Point

But oh well.

You know how change in entropy $$dS$$ of a closed system assuming reversibility of the processes = $$(\frac{dQ}{T})_{rev}=\frac{C_{p}dT}{T}$$

So when you try to find the actual entropy with respect to temperature, it's:

$$\displaystyle \int S_{T} = S_{0} + \int^{T}_{0} \C_{p}dT/T\$$

That's understandable. But that's my derivation. The text uses a slightly different formula:

$$S_{T} = S_{0} + \int^{T}_{0} \\frac{C_{p}dT}{T}\ + \sum \frac{\Delta H_{trans}}{T}$$

So my question 1 is: where did the $$\sum \frac{\Delta H_{trans}}{T}$$ come from?

And my question 2 is:
if we say that heat capacity $$C_{p}$$ is constant (it's not strictly constant, but with an approximation, we can call it a constant), we have:

$$\int \frac{C_{P}dT}{T} \sim C_{P} \int \frac{dT}{T}=$$
$$\sim C_{P} \ln{T}$$

Could the top eqn. be used as an approximation (part of an approximation, this is only a part of the equation)

As you can tell I am not that well-versed in Latex D=

Thanks

~Tosser

The $\Delta H/T$ terms come from the phase transitions from solid-to-liquid and from liquid-to-vapor (and any other phase transitions that occur, as, for example, from different crystal forms).