Consider the following liquid-vapour equilibrium

$Liquid space rightwards harpoon over leftwards harpoon space Vapour$
Which of the following relations is correct?

$dlnP over dT equals fraction numerator negative increment H subscript v over denominator R T end fraction$
$dlnP over dT squared space equals space fraction numerator negative increment straight H subscript straight v over denominator straight T squared end fraction$
$dlnP over dT space equals space fraction numerator negative increment straight H subscript straight v over denominator RT squared end fraction$
$dlnG over dT space equals space fraction numerator negative increment straight H subscript straight v over denominator RT squared end fraction$

Solution

dlnP over dT space equals space fraction numerator negative increment straight H subscript straight v over denominator RT squared end fraction

The given phase equilibria is
$Liquid space rightwards harpoon over leftwards harpoon space Vapour$
This equilibrium states that, when liquid is heated, it converts into vapour but on cooling, it further converts into liquid, which is derived by Clausius clapeyron and the relationship is written as,

$dlnP over dT space equals space fraction numerator negative increment straight H subscript straight v over denominator RT squared end fraction where space increment straight H subscript straight v space equals space Heat space of space vaporisation$