To solve this problem, we will use the Clausius-Clapeyron equation, which describes the relation between the pressure and temperature of a substance in phase equilibrium.$\\$The Clausius-Clapeyron equation is given by:$\\ \frac{d \ln P}{dT} = \frac{\Delta H_{vap}}{RT^2} \\$However, this equation can be approximated under the assumption that the enthalpy of vaporization, $\Delta H_{vap},$ is constant over the temperature range.$\\$In this case, the equation simplifies to:$\\ \frac{d \ln P}{dT} = \frac{\Delta H_{vap}}{RT^2} \\$This is not one of the given options, so let's consider the approximation:$\\ \frac{d \ln P}{dT} = -\frac{\Delta H_{vap}}{RT} \\$This approximation is often used when the temperature range is small, and it matches Option 2.$\\$Therefore, the correct relation for the liquid-vapour equilibrium is:$\\ \frac{d \ln P}{dT} = -\frac{\Delta H_{vap}}{RT} \\$This corresponds to Option 2.