Problem $1.(15$ pts$)$ A rigid tank of volume $2$ m$^3$ initially contains air at $0\mathrm{.}1$ bar, $290$ K$.$ A leak develops, and air flows in slowly from the surroundings which are at $1\mathrm{.}1$ bar, $312$ K$.$ After the tank and its surroundings come to equilibrium, and assuming the air is an ideal gas with constant specific heats evaluated at $300$ K$,$ determine:

$(3$ pts$)$ What is the final temperature in the tank, in $\backslash$deg C$?$

$(4$ pts$)$ How much mass has entered the tank, in kg$?$

$(8$ pts$)$ What is the amount of energy transfer by heat for a control volume that encloses the tank, in J$?$