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## Homework Statement

Show that the second law of thermodynamics predicts the spontaneous freezing of liquid water at -5[tex]^{o}[/tex]C under 1 bar of constant pressure. Assume that Cp is temperature independent.

Standard water fusion enthalpy = 6.008 kJ/mol @ 273.15 K

[tex]\geq[/tex] has to be interpreted as greater than, not greater or equal, in this example.

## Homework Equations

A: [tex]dS[/tex] [tex]\geq[/tex] [tex]\frac{\partial q}{T}[/tex]

B: [tex]\Delta[/tex][tex]S_{transition}[/tex] = [tex]\frac{\Delta H_{transition}}{T_{transition}}[/tex]

C: [tex]\Delta S = \int \frac{Cp}{T} dT[/tex]

D: [tex]\Delta H = q[/tex] in an isobaric process

## The Attempt at a Solution

After having wasted an hour or so on this presumably easy problem, I cannot get the second law to predict the freezing.

[tex]Cp\ ln(T) \geq \frac{\Delta H_{transition}}{T_{transition}}[/tex] ?

Some advice would be appreciated. I know the proof is simple. I'm having some brain fog atm though.

Thanks!