Understanding the Derivation of the Latent Heat and Entropy Equation

[WWCY]

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

 

[BvU]

Could someone assist me

Look at the dimensions of your variables

 

[mjc123]

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?

 

[WWCY]

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)?

 

[mjc123]

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.