Gibbs phase rule

$F=C-P+2$

states that a one component $(C=1)$ one phase $(P=1)$ system has two degrees of freedom $(F=2).$ The number of degrees of

freedom is the number of independent intensive variables, i$.$e$.$ the largest number of thermodynamic parameters such as

temperature or pressure that can be varied simultaneously and arbitrarily without determining one another. If we choose two

independent state variables $T$ and $p$ to describe the state of a system $($one phase, one component, one mole$)$ then

$H(T,p)$

and

$dH=(\frac{\text{d}\text{e}\text{l}\text{H}}{\text{d}\text{e}\text{l}\text{T}}{)}_{p}dT+(\frac{\text{d}\text{e}\text{l}\text{H}}{\text{d}\text{e}\text{l}\text{p}}{)}_{T}dp$

a$)$ Define the equation that enables the practical measurement of $(\frac{\text{d}\text{e}\text{l}\text{H}}{\text{d}\text{e}\text{l}\text{p}}{)}_T$ and Joule$-$Thomson Coefficient. $(2$ marks, K&U

$2\mathrm{.}3$

b$)$ What happens with the temperature of a van der Waals gas during constant enthalpy expansion if $T.$ Choose the

correct answer $(3$ marks, $K$&$U2\mathrm{.}3)$:

$i.$ Temperature $of$ a van der Waals gas increases.

$ii.$ Temperature $of$ a van der Waals gas decreases.