Entropy Equatio for a closed system

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Main Question or Discussion Point

I must have already been banned for spamming threads.

But oh well.

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

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

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

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

[tex]S_{T} = S_{0} + \int^{T}_{0} \\frac{C_{p}dT}{T}\ + \sum \frac{\Delta H_{trans}}{T}[/tex]

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

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

[tex]\int \frac{C_{P}dT}{T} \sim C_{P} \int \frac{dT}{T}=[/tex]
[tex]\sim C_{P} \ln{T}[/tex]

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
 

Answers and Replies

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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).
 

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