Problem $3-$ Application of first law to closed systems $(27\mathrm{.}5$ pts$)$

Dr$.$ Bach's bicycle tire has a volume of $0\mathrm{.}03m^3.$ State $1$ : He filled the tire with compressed air at $T_1=25C$ to $p_1=4\mathrm{.}5$ bar. His mischievous cousin "borrowed" a parabolic mirror from the physics department to concentrate sunlight on the tire to burst it$.$ The tire's burst pressure at $T_2$ is $p_2=9$ bar.

Additional known properties:

Specific gas constant for air: $R_a=0\mathrm{.}287k\frac{J}{k}g-K$; Constant $c_v$ of $0\mathrm{.}72k\frac{J}{k}g-K$

Fill out the table below:

$\backslash$table$[[$a$)$ Mass of the air in the tire $m_1=m_2=m,0\mathrm{.}1578,$kg$],[$b$)$ Final tire temperature $T_2$ at which the tire will burst,$323\mathrm{.}14,C$