= Solution
{c}
Let $Y=-\ln(p/p_*)$. For the temperature-dependent <latent heat>,
$$
Y(T)=\begin{cases}
\dfrac{L_s}{R_{\rm wv}}\left(\dfrac1T-\dfrac1{T_*}\right),&T\leq T_*,\\[4pt]
K\left[T_c\left(\dfrac1T-\dfrac1{T_*}\right)+\ln\dfrac T{T_*}\right],&T_*\leq T<T_c.
\end{cases}
$$
Keeping the <latent heat> of vaporization fixed changes only the upper branch to
$$
Y_{\rm fixed}(T)=\frac{L_*}{R_{\rm wv}}\left(\frac1T-\frac1{T_*}\right).
$$
Both curves fall from $+\infty$ as $T\to0^+$, pass through $Y=0$ at the <triple point>, and are convex. At the <triple point> there is a corner because the <latent heat> changes from $L_s$ to $L_*$. Their right-hand slopes there agree. Above the <triple point>,
$$
Y'_{\rm variable}=-K\frac{T_c-T}{T^2},\qquad
Y'_{\rm fixed}=-\frac{L_*}{R_{\rm wv}T^2},\qquad
Y''_{\rm variable}=K\frac{2T_c-T}{T^3}>0.
$$
The variable-<latent heat> curve lies \b[above] the fixed-<latent heat> curve: its downward slope has smaller magnitude at every $T>T_*$. It reaches a horizontal tangent at $T_c$, whereas the fixed-<latent heat> curve is still descending. Both limiting ordinates are finite; this model gives $Y_{\rm variable}(T_c)\simeq-7.30$ and $Y_{\rm fixed}(T_c)\simeq-11.40$. These are extrapolations of the stipulated model, not accurate <water> <liquid-gas critical point> data. Extending the variable branch beyond $T_c$ would give negative <latent heat> and is physically inadmissible.
\Image[/past-exam-of-the-physics-of-atmospheres-and-oceans-course-of-the-university-of-oxford/2022-saturation-pressure.png]
{title=Integrated saturation curves for fixed and temperature-dependent latent heat}
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