A sample consisting of $2$ moles of an ideal gas is expanded isothermally at $22C$ from $22\mathrm{.}8d{m}^3$ to $31\mathrm{.}7d{m}^3.$

$($a$)$ Calculate the heat exchanged and the change of entropy if this expansion occurs reversibly.

$($b$)$ Calculate the final pressure of the gas after this expansion.

$($c$)$ In a second step, the gas is then expanded isothermally from $31\mathrm{.}7d{m}^3$ against a constant external pressure of $1\mathrm{.}0{10}^{5}Pa$ until the equilibrium is reached. Calculate the work performed in this second step.