Problem $3(25$ points$)$

A poorly insulated rigid tank with volume $=1m^3$ contains saturated water vapor initially at a pressure of $300$ kPa $.$ A line carrying steam at $1000$ kPa and $500C$ is connected to the tank and $2$ kg of steam are let into the tank through a valve until the final tank pressure is $500$ kPa $.$

a$)$ How much heat is gained or lost by the contents of the tank during this process?

b$)$ Is this heat transfer into or out of the tank?

c$)$ What is the final temperature of the contents?