Problem $1$: $(15$ pts $)$ A rigid tank of volume $2m^3$ initially contains air at $\frac{0\mathrm{.}21}{b}ar,290K.$ A leak develops, and air flows in slowly from the surroundings which are at $\frac{1\mathrm{.}1}{b}ar,312K.$ After a while, the tank and its surroundings come to equilibrium. Neglecting kinetic and potential energy effects, and assuming the air is an ideal gas with constant specific heats evaluated at $300$ K $,$ determine:

a$)(3$ pts