The relationship between vapor pressure ($P$) and temperature ($T$) for a liquid-vapor equilibrium is given by the Clausius-Clapeyron equation.

1. Concept: For the equilibrium $Liquid \rightleftharpoons Vapour$, the equilibrium constant $K_p$ is equal to the vapor pressure $P$ (assuming pure liquid).
2. Temperature Dependence: The variation of the equilibrium constant with temperature is given by the van't Hoff equation: $\frac{d \ln K}{dT} = \frac{\Delta H^\circ}{RT^2}$.
3. Substitution: Substituting $K = P$ and $\Delta H^\circ = \Delta H_{vap}$ (Enthalpy of vaporization, $\Delta H_v$), we get: $\frac{d \ln P}{dT} = \frac{\Delta H_v}{RT^2}$

This equation quantitatively describes how vapor pressure increases with temperature for an endothermic process (vaporization).