Answer
The temperature of the air would increase by $57.5~C^{\circ}$, so the new temperature of the air would be $77.5~^{\circ}C$
Work Step by Step
We can find the number of moles of nitrogen:
$PV = nRT$
$n = \frac{PV}{RT}$
$n = \frac{(1.01\times 10^5~Pa)(8000~m^3)}{(8.314~J/mol~K)(293.15~K)}$
$n = 3.315\times 10^5~mol$
We can find the total energy that heats the gas:
$Q = (501)(110~W)(7200~s) = 3.968\times 10^8~J$
We can find the change in temperature:
$Q = c~n~\Delta T$
$\Delta T = \frac{Q}{c~n}$
$\Delta T = \frac{3.968\times 10^8~J}{(20.8~J/mol~C^{\circ})(3.315\times 10^5~mol)}$
$\Delta T = 57.5~C^{\circ}$
The new temperature of the air will be $20.0^{\circ}C+57.5~C^{\circ}$ which is $77.5~^{\circ}C$.
