A$3)$ Air at $\backslash (5^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ is contained in a well$-$insulated rigid tank, with a volume of $\backslash (0\mathrm{.}2\backslash$mathrm$\{$~m$\}^\{3\}\backslash ).$ The tank is fitted with a paddle wheel that transfers energy to the air at a constant rate of $4\mathrm{.}0$ W $,$ for twenty $(20)$ minutes. The initial density of the air is $\backslash (1\mathrm{.}2\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ If no changes in kinetic or potential energy occur, determine:

a$)$ the density of the air after the elapsed time $($provide$/$state justification$)$;

b$)$ the change in the total and specific internal energy of the air $\backslash ([\backslash$mathrm$\{$kJ$\}],[\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}]\backslash )$;

c$)$ the initial pressure of the air in the tank $[$kPa$($g$)]$ and $[$kPa$($abs$)].$