Physics Asked on March 3, 2021
Blundell and Blundell writes
$$
frac{mathrm{d} p}{mathrm{~d} T}=frac{s_{2}-s_{1}}{v_{2}-v_{1}}$$ where $s_1$,$s_2$ are the entropy per particle in phase 1 and 2 and $v_1$,$v_2$ are the entropy per particle in phase 1 and 2
If we define latent heat per particle as $l=T Delta s,$ we then have
$$
frac{mathrm{d} p}{mathrm{~d} T}=frac{l}{Tleft(v_{2}-v_{1}right)}$$ or equivalently
$frac{mathrm{d} p}{mathrm{~d} T}=frac{L}{Tleft(V_{2}-V_{1}right)}$
This is the Clausius-Clapeyron equation.
How can we go from the second equation to the third? How did the author change the specific quantities to absolute ones?
Edit: Many comments say that just multiply it by the number of moles and you’ll get the final equation. But in order to get the final equation I’ve to multiply $v_1$ by $n_1$ and $v_2$ by $n_2$ ,where $n_1$ and $n_2$ refer to the number of moles in each phase.
That can’t be achieved by multiplying the numerator and denominator by the same term.
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