$2\mathrm{.}2$ A convergent$-$divergent nozzle has an efficiency of $89\%.$ The gas with negligible inlet velocity has the adiabatic index and gas constant of $1,4$ and $0,2875k\frac{J}{k}g.K.$ At the throat, the pressure is $1,58$MPa. At the exit, the actual temperature is $494$ kelvin. Across the nozzle, the isentropic temperature drop is $300$ kelvin.

From this information, determine each of the following:

$2\mathrm{.}2\mathrm{.}1$ The absolute temperature in kelvin and pressure in kPa at the nozzle inlet

$2\mathrm{.}2\mathrm{.}2$ The gas constant$-$pressure specific heat capacity

$2\mathrm{.}2\mathrm{.}3$ At the throat: the temperature in kelvin, velocity in $\frac{m}{s},$ and volume in $\frac{m^3}{k}g$

$2\mathrm{.}2\mathrm{.}4$ The isentropic temperature in kelvin at the nozzle exit