QA$2.7$ moles of methane are initially at a pressure of $2$ bar and a temperature of

$290$ K$.$ Calculate the enthalpy change of a process after which the gas has a

pressure of $6$ bar and a temperature of $420K.$ You can make use of the fact

that the enthalpy is a function of state to define a convenient path for the

process. You can also assume that under these conditions methane

behaves ideally and has heat capacities of $c_P=35\mathrm{.}7Jmo{l}^{-1}{K}^{-1}$ and

$c_V=27\mathrm{.}4Jmo{l}^{-1}{K}^{-1}.$

$[20$ marks$]$