$1.$ The gas turbine uses $3$ kg $/$ s of hot air, which enters with pressure and heat of $4$ bar, $760\backslash$deg C$,$ exits the exhaust at $400\backslash$deg C and produces heat losses from the generator body of $15$ kW$.$

$2.$ The air temperature is $1005$ J $/$ kg$.$ K$,$ the kinetic energy and the potential energy were neglected.The mass flow rate in gas turbine system vary through operation which led to make change on the values of pressure, volume and temperature in the system according to that complete the following:

$4.$ Drive steady flow energy equations from $1$st principles.