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In a car tire, which is assumed to have a constant volume of $0\mathrm{.}03$m$^3,$ there is air at $15$C with a gauge pressure of $170$kPa the ambient pressure is $1$bar$1.$The air is supplied with heat of $2\mathrm{.}7$kJ through solar radiation.. The air is assumed to behave as an ideal gas $($Cp$=1\mathrm{.}01$kJ$/$kg$*$K $,$ $=1\mathrm{.}4,$ molar mass $=28\mathrm{.}96$g$/$mol$.$

$($a$)$ What air temperature is established in the tire $($C$)?$

$($b$)$ What tire gauge pressure occurs $($in MPa$)?$

$($c$)$ How does the internal enthalpy of the tire contents change $($in kJ$)?$

$($d$)$ How much air mass needs to be released to restore the original tire pressure $($keeping the temperature unchanged$)($in g$)?$