= Solution
Rename the <Antoine equation> coefficients $A_A,B_A,C_A$ to distinguish them from the heat-capacity constants. The logarithmic slope is independent of the <pressure> unit:
$$
\frac{d\ln p_{\rm sat}}{dT}=\ln(10)\frac{B_A}{(T+C_A)^2}.
$$
Using an ideal vapour and neglecting liquid specific volume, Clausius–Clapeyron gives $d\ln p_{\rm sat}/dT=L_v/(R_vT^2)$. Therefore the positive magnitude of the <latent heat> released on <condensation> is
$$
\boxed{L_v(T)=R_v\ln(10)B_A\left(\frac{T}{T+C_A}\right)^2.}
$$
For $C_A=-198.043\,\mathrm K$, $d\ln L_v/dT=2C_A/[T(T+C_A)]<0$ over the quoted range. With $R_v\simeq461.5\,\mathrm{J\,kg^{-1}\,K^{-1}}$, this fit implies approximately $2.984\,\mathrm{MJ\,kg^{-1}}$ at $380\,\mathrm K$ and $1.598\,\mathrm{MJ\,kg^{-1}}$ at $573\,\mathrm K$. The required ratio does not depend on $R_v$:
$$
\boxed{\frac{L_v(573)}{L_v(380)}=
\left[\frac{573(380-198.043)}{380(573-198.043)}\right]^2\simeq0.5354.}
$$
The decreasing trend is qualitatively consistent with the liquid and vapour phases becoming less distinct towards the <liquid-gas critical point>. However, the full Clapeyron relation is $L_v=T(v_v-v_l)\,dp_{\rm sat}/dT$: at criticality the two specific volumes merge and the <latent heat> vanishes. Neglecting $v_l$ and treating the vapour as ideal then fail. The Antoine coefficients are not licensed for extrapolation beyond $573\,\mathrm K$, and <derivatives> of an approximate <pressure> fit can be less accurate than the fitted <pressures> themselves.
A concrete check exposes the extrapolation failure: at the supplied $647\,\mathrm K$ critical <temperature> the formula would still give $L_v\simeq1.42\,\mathrm{MJ\,kg^{-1}}$, rather than zero, and $p_{\rm sat}\simeq134\,\mathrm{bar}$ rather than $221\,\mathrm{bar}$. Above the true <liquid-gas critical point> there is no liquid–vapour coexistence curve or <condensation> <latent heat> in the same sense. The last panel of the original figure in <past-exam-of-the-physics-of-atmospheres-and-oceans-course-of-the-university-of-oxford/2018/1/b/solution> makes this limitation visible.
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