Latent Heat Solid->gas Liquid->gas transitions

In summary, the equations and constants provided can be used to show that in transitions from solid to gas and liquid to gas at temperatures much lower than the critical temperature, the specific latent heat L can be approximated by a linear function of temperature, with constants a and b. The problem also involves using the calorific coefficient and cubic expansion coefficient to rearrange and integrate an equation, with the hint that v_1 is much smaller than v_2. The method for solving this problem is not explicitly given, but it may involve separating variables or using another approach.
  • #1
thonwer
60
0

Homework Statement


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

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 gas and 1 is for solid or liquid
[itex] cp , \alpha [/itex] are the calorific coefficient at constant pressure and the cubic expansion coefficient.

3. The Attempt at a Solution
Honestly, I do not have any idea of how to start, I only got to say that [itex] v_1 \ll v_2 [/itex].
 
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  • #2
Try rearranging the equation given in 2.), Relevant equations, and integrating.
 
  • #3
Can I separate variables? Or do I have to use another method?
 

Related to Latent Heat Solid->gas Liquid->gas transitions

1. What is latent heat and how does it affect solid-to-gas and liquid-to-gas transitions?

Latent heat is the amount of energy required to change the state of a substance without changing its temperature. During solid-to-gas and liquid-to-gas transitions, this energy is used to break the bonds between molecules, allowing them to change from a more ordered state to a more disordered state.

2. What factors influence the amount of latent heat needed for a solid-to-gas or liquid-to-gas transition?

The amount of latent heat required for a transition depends on the substance's specific heat capacity, the amount of substance being transitioned, and the surrounding temperature and pressure.

3. How does the rate of temperature change affect the solid-to-gas and liquid-to-gas transitions?

The rate of temperature change can affect the transitions by determining the amount of heat that can be transferred within a given time frame. A slower temperature change may allow for more of the substance to transition, while a faster temperature change may not allow for enough heat to be transferred for the transition to occur.

4. Can latent heat be recovered during a reverse transition, such as gas-to-liquid or gas-to-solid?

Yes, the same amount of latent heat that was released during the solid-to-gas or liquid-to-gas transition can be absorbed during the reverse transition, allowing for the substance to return to its original state.

5. How do changes in pressure affect the solid-to-gas and liquid-to-gas transitions?

Changes in pressure can affect the transitions by altering the boiling point of the substance. In a higher pressure environment, the substance's boiling point will be higher, meaning more energy will be required to transition from a liquid to a gas state.

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