= Integrated Clausius-Clapeyron relation
{c}
{title2=$\ln(p_2/p_1)\simeq-(L_m/R)(1/T_2-1/T_1)$}
If the molar <latent heat> $L_m$ is approximately constant on the chosen <temperature> interval, the <Ideal-vapor Clausius-Clapeyron approximation> integrates to
$$
\ln\frac{p_2}{p_1}\simeq-\frac{L_m}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right),\qquad p(T)\simeq p_1\exp\left[\frac{L_m}{R}\left(\frac{1}{T_1}-\frac{1}{T}\right)\right].
$$
For $L_m>0$, higher absolute <temperature> gives higher <saturation pressure>. A plot of $\ln(p/p_1)$ against <inverse temperature> $1/T$ is a straight line of slope $-L_m/R$. One reference pair $(T_1,p_1)$ fixes its intercept. On a per-unit-<mass> basis replace $L_m/R$ by $L/R_s$, with $R_s=R/M$ and $M$ the <molar mass>; using $L$ in $\mathrm{J\,kg^{-1}}$ with the molar $R$ would give incompatible units.
If only the constant-<latent heat> approximation is relaxed, the same ideal-vapor model instead gives
$$
\ln\frac{p_2}{p_1}\simeq\frac{1}{R}\int_{T_1}^{T_2}\frac{L_m(T)}{T^2}\,dT.
$$
Consequently an apparent straight-line fit across a broad <temperature> range need not represent a single material constant. The simple exponential also approaches a finite value as $T\to\infty$; this is a property of the stipulated formula, not a prediction that <liquid>–<gas> <phase coexistence> extends beyond a <thermodynamic critical point>.
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