Understanding the Derivation of the Latent Heat and Entropy Equation

In summary, the conversation discusses the equation ##L / T = \Delta S## and its derivation. The individual explains their confusion with the equation and the incorrect result they obtained after substitution. The other individual clarifies that the equation compares specific latent heat with total entropy change, which is why the result is not sensible. They suggest working with either total or specific quantities and not mixing them up.
  • #1
WWCY
479
12

Homework Statement


I came across this equation ##L / T = \Delta S## and am not too sure about its derivation.

From what I know, ##L = Q/m## and ##Q = TdS ##.

Substitution gives me ##\Delta S = mL / T## which isn't correct.

Could someone assist me in understanding the derivation?

Thanks!

Homework Equations

The Attempt at a Solution

 
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  • #2
WWCY said:
Could someone assist me
Look at the dimensions of your variables
 
  • #3
WWCY said:
From what I know, L=Q/m and Q= TdS .
That's giving you dS as the total entropy change of the sample, but L as the specific latent heat (i.e. per unit mass). You're comparing apples and oranges, no wonder you don't get a sensible answer.
What do you know, in terms of energetics, about the equilibrium at the melting point?
 
  • #4
mjc123 said:
That's giving you dS as the total entropy change of the sample, but L as the specific latent heat (i.e. per unit mass).

Am I mixing latent heat (total heat) with specific latent heat (heat / unit mass)?
 
  • #5
Yes. work with total quantities (not usually useful for a general statement like your equation), or specific quantities, or molar quantites, but don't mix them up. It looks like you're just quoting formulae without understanding them.
 

FAQ: Understanding the Derivation of the Latent Heat and Entropy Equation

What is latent heat and how does it relate to temperature?

Latent heat refers to the heat energy that is absorbed or released during a phase change of a substance, such as from a solid to a liquid or from a liquid to a gas. This heat energy does not change the temperature of the substance, but rather, is used to break or form intermolecular bonds between particles. This means that latent heat and temperature are closely related, but not interchangeable.

What is the difference between latent heat of fusion and latent heat of vaporization?

The latent heat of fusion is the heat energy required to change a substance from a solid to a liquid, while the latent heat of vaporization is the heat energy required to change a substance from a liquid to a gas. This means that the latent heat of vaporization is typically higher than the latent heat of fusion, as it takes more energy to break the stronger bonds between liquid particles compared to solid particles.

How does entropy relate to the concept of latent heat?

Entropy is a measure of the disorder or randomness of a system. When a substance undergoes a phase change, such as from a solid to a liquid, the particles are able to move more freely and therefore the entropy of the system increases. This means that as latent heat is absorbed or released during a phase change, the entropy of the system also changes.

Can latent heat be used to calculate the change in temperature of a substance?

No, latent heat cannot be used to calculate the change in temperature of a substance. As mentioned earlier, latent heat is used to break or form bonds between particles during a phase change, and does not contribute to a change in temperature. To calculate the change in temperature, the specific heat capacity of the substance must be used instead.

How is latent heat and entropy important in industrial and environmental processes?

Understanding the concepts of latent heat and entropy is crucial in many industrial and environmental processes. For example, in refrigeration and air conditioning systems, the latent heat of vaporization is used to remove heat from a space. In environmental processes such as cloud formation and precipitation, the release of latent heat during condensation plays a crucial role in atmospheric dynamics.

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