A perfect gas and $=2$ flows through a duct and enters a turbine

with a pressure of $50$ kPa and temperature of $600$ K $.$ The turbine extracts $10$ MW

from the flow and $2$ MW of heat is lost to the environment during the process. The

gas exits the turbine with a pressure of $40$ kPa and a temperature of $300$ K $.$

Assume gravitational effects are negligible and the inlet and outlet velocities are

the same.

$($a$)$ Determine the ratio of the inlet duct cross$-$sectional area to the

outlet duct cross$-$sectional area $($A$1/$ A$2).$

$($b$)$ Determine the mass flow rate through the system.