$2.[10$ Pts$]$ A circular rubber balloon $($insulated$)$ contains air at $300$ K and $100$ kPa $.$ In an internally reversible

process, the balloon expands after receiving an unknown amount of heat. The final volume is two times that of

the initial balloon, and the specific entropy of the system increases by $0\mathrm{.}3(($kJ$))/(($kg$)*($K$)).$ Treat air as an ideal gas and

ignore rubber. Use absolute zero as the reference point.

$($a$)$ What is the final pressure of the air in the balloon? $[5$ Pts$]$

$($b$)$ How much specific heat does this process require if the process is polytropic? $[5$ Pts$]$