air enters a horizontal constant$-$diameter heating duct operating at a steady state at $300$K$,1$ bar, with a volumetric flow rate of $0\mathrm{.}25$m$^3/$s and exits at $325$K$,0\mathrm{.}95$ bar. the flow area is $0\mathrm{.}04$m$^2.$ Assuming the ideal gas model with k$=1\mathrm{.}4$ for the air, determine:

a$)$ the mass flow rate in kg$/$s

b$)$the velocity at the inlet and exit each in m$/$s$,$ and

c$)$ the rate of heat transfer to the air in kW