$(20$ pts$)$ Two tanks are connected by a valve. One tank initially contains $2$ kg of air at $77C$ and $70$ kPa $.$ The other tank holds $6$ kg of air at $27C$ and $120$ kPa $.$ The valve is opened and the gases are allowed to mix while receiving energy by heat transfer from the surroundings. The final equilibrium temperature is $47C.$ Use the ideal gas model.

Determine

a$)$ the final equilibrium pressure;

b$)$ the heat transfer for the process in kJ $.$