$(24$ points$)$ A spherical balloon of diameter $0\mathrm{.}7$ m is filled with a helium$-$argon mixture at

$20\backslash$deg C and $130$ kPa. The mixture can be assumed in this problem as an ideal gas, with

specific heat ratio of $1\mathrm{.}67$ and gas constant of $1\mathrm{.}53$ kJ$/$kg$*$K$.$

$($a$)(6$ points$)$ Determine the constant pressure and constant volume specific heats of the

mixture, in kJ$/$kg$*$K$.$

$($b$)(4$ points$)$ Determine the mass of gases in the balloon.

$($c$)(10$ points$)$ Now suppose the temperature of the surrounding air decreases by $10$

degrees, and the balloon reaches thermal equilibrium with this air. During this process

the balloon loses $10\%$ of its original volume. Determine the new pressure in the

balloon.

$($d$)(4$ points$)$ Determine the internal energy change in this process