Problem $1(35$ points$)$

A piston$-$cylinder device contains a mixture of $0\mathrm{.}5$ kg of $H_2$ and $1\mathrm{.}2$ kg of $N_2$ at $100$ kPa and $300$

K $.$ Heat is now transferred to the mixture at constant pressure until the volume is doubled.

Assuming an ideal gas mixture, determine:

a$.$ the amount of heat transfer in kJ $.$

b$.$ the entropy variation $s$ of the mixture in $k\frac{J}{K}.$