$12.($Piston Cylinder $25$ points$)$ A piston$-$cylinder device is filled with air. The piston is resting on a set of stops. There is $0\mathrm{.}73$ kg of gas at $125$ kPa and $\backslash (27^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The mass of the piston and outside pressure is such that $\backslash (\backslash$mathrm$\{$Sl$\}^\{2\}\backslash$mathrm$\{$kPa$\}\backslash )$ of pressure is required to raise it$.$ How much heat must be transferred to the gas $516\mathrm{.}7$ kP $9$ before the piston starts rising?

You may use the ideal gas tables provided for air to solve this problem assuming air acts as an ideal gas.