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Daria
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- Homework Statement
- The free energy per unit volume of a liquid is measured to be
FL/V=a(T)ρ2/2
Where ρ is a number density, a(T)=α/T with α a constant.
The free energy of the solid phase is
Fs/V=b(T)ρ3/3 with b(T)= β/T with β a constant.
At a given temperature, the pressure of the liquid can be increased to reach a value Ps at which the liquid solidifies. The density of the liquid is ρL at the transition, the density of the coexisting solid is ρS
1) Determine ρL, ρS and Ps as a function of temperature.
2) What is the change in the molar entropy across the transition?
3) Use Clapeyron’s relation to obtain the slope of the solidification curve. Is this consistent with the result obtained in 1) for P?
- Relevant Equations
- dP/dT = ΔS/ ΔV = ΔH/(TΔV)
F=U-TS
dF=-PdV-SdT
Hello! I'm struggling with this exercise for three days already. Would appreciate any help. Thanks in advance. This is my thoughts...
So a number density ρ=N/V. As I understand N doesn’t change through transition, but V changes
The free energy F=U-TS or dF=-PdV-SdT
As the liquid coexists with the solid, the liquid and solid free energy functions have the common tangent. I found derivatives for FL and Fs (I thought it is connected with a common tangent, but it didn’t help me with anything)
Clapeyron’s relation: dP/dT = ΔS/ ΔV = ΔH/(TΔV)
This is everything I came up with during the brainstorm and I don’t know if any of this is right, I don’t understand what to do next and what direction to go :’(
So a number density ρ=N/V. As I understand N doesn’t change through transition, but V changes
The free energy F=U-TS or dF=-PdV-SdT
As the liquid coexists with the solid, the liquid and solid free energy functions have the common tangent. I found derivatives for FL and Fs (I thought it is connected with a common tangent, but it didn’t help me with anything)
Clapeyron’s relation: dP/dT = ΔS/ ΔV = ΔH/(TΔV)
This is everything I came up with during the brainstorm and I don’t know if any of this is right, I don’t understand what to do next and what direction to go :’(