Latent Heat in Solid-->Liquid transitions (phase change)

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SUMMARY

The discussion centers on demonstrating that the latent heat (L) remains approximately constant during solid to liquid phase transitions at temperatures significantly lower than the critical temperature (Tc). The relevant equation involves the specific heat capacities (cp1 and cp2) and the volumetric thermal expansion coefficients (α1 and α2). A suggestion is made to utilize the Clapeyron equation to relate pressure and temperature changes along the solid-liquid equilibrium line, which is crucial for solving the differential equation presented.

PREREQUISITES
  • Understanding of phase transitions, specifically solid to liquid transitions.
  • Familiarity with the Clapeyron equation and its application in thermodynamics.
  • Knowledge of specific heat capacity (cp) and volumetric thermal expansion coefficients (α).
  • Ability to solve differential equations in the context of thermodynamic properties.
NEXT STEPS
  • Study the Clapeyron equation and its implications for phase transitions.
  • Learn about the relationship between latent heat and temperature in phase changes.
  • Explore the derivation and applications of the equation involving specific heat capacities and thermal expansion coefficients.
  • Investigate numerical methods for solving differential equations related to thermodynamic processes.
USEFUL FOR

Students and professionals in thermodynamics, particularly those studying phase transitions and latent heat, as well as researchers focusing on material properties during phase changes.

thonwer
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Homework Statement


Show that in Solid to Liquid transitions at [itex]T \ll {T}_{c} , L\simeq constant[/itex] where [itex]{T}_{c}, L[/itex] are the critic temperature and latent heat respectively.

Homework Equations


[itex]\left( \frac{d ( \frac {L} {T})} {dT} \right) = \frac {{c}_{p2}-{c}_{p1}} {T}+ \frac {\alpha_1v_1-\alpha_2v_2} {v_2-v_1} \frac {L} {T}[/itex]

2 is for liquid and 1 is for solid
cp,α are the calorific coefficient at constant pressure and the cubic expansion coefficient.

The Attempt at a Solution


For example with ice and water, I assume [itex]v_2 \simeq v_1[/itex] and then I try to solve the differential equation but I don't get to [itex]L\simeq constant[/itex].

Can anybody help me please?
 
Physics news on Phys.org
Consider using the Clapyron equation which relates the changes in pressure and temperature along the equilibrium line between solid and liquid.

Chet
 

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