A mole of ideal gas has $1500$ kJ of heat added to it$,$ causing it to expand irreversibly from $5\mathrm{.}0$ m$3$ to $12\mathrm{.}5$ m$3,$ against a pressure of

$2\mathrm{.}0\backslash$times $105$ Pa$.$

$($i$)$ State the First Law of Thermodynamics, giving an appropriate equation.

$(2$ marks$)$

$($ii$)$ Explain, briefly, what is meant by the term state function and give an example of such a function.

$(2$ marks$)$

$($iii$)$ What is the change in the internal energy of the system?

$(4$ marks$)$

$($iv$)$ What is the change in temperature of the gas?

$(2$ marks$)$