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

Clapyron equation.In summary, the conversation is about showing that in Solid to Liquid transitions at T \ll {T}_{c}, the latent heat L remains constant. The homework equations involve the calorific coefficient and cubic expansion coefficient, and the attempt at a solution involves using the Clapyron equation. Chetan offers help and suggests using the Clapyron equation to solve the given equation.
  • #1
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?
 
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  • #2
Consider using the Clapyron equation which relates the changes in pressure and temperature along the equilibrium line between solid and liquid.

Chet
 

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

1. What is latent heat in solid to liquid transitions?

Latent heat in solid to liquid transitions refers to the energy required to change the state of a substance from solid to liquid without changing its temperature. This energy is used to break the intermolecular bonds within the solid, allowing it to transition to a liquid state.

2. How is latent heat calculated?

Latent heat is calculated by multiplying the mass of the substance by its specific latent heat, which is a constant value determined experimentally. The equation is Q = m * L, where Q is the latent heat, m is the mass, and L is the specific latent heat.

3. What factors affect latent heat in solid to liquid transitions?

The main factor that affects latent heat in solid to liquid transitions is the type of substance. Each substance has a different specific latent heat due to the strength of its intermolecular bonds. Other factors that may affect it include pressure, temperature, and impurities in the substance.

4. How does latent heat play a role in everyday life?

Latent heat plays a role in everyday life in many ways. For example, without latent heat, ice would not melt into water, and we would not be able to cook food using water as a medium. The process of sweating also involves latent heat, as our body uses it to convert sweat from liquid to gas, thus cooling us down.

5. Can latent heat be used to store energy?

Yes, latent heat can be used to store energy. This is known as latent heat storage, and it involves using substances with high specific latent heat, such as water, to store heat energy. This energy can then be released when the substance transitions from liquid to solid, providing a sustainable source of energy.

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