A calorically perfect gas (specific heat at constant pressure $$1000$$$$J/kg.K$$) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are $$1100K$$ and $$400K.$$ respectively. The power produced is $$4.6MW$$ and heat escapes at the rate of $$300kJ/s$$ through the turbine casing. The mass flow rate of the gas (in $$kg/s$$) through the turbine is.

One $$kg$$ of an ideal gas (gas constant, $$R = 400$$ $$J/kg.K;$$ specific heat at constant volume, $${c_v} = 1000\,J/kg.K$$ at $$1$$ bar, and $$300$$ $$K$$ is contained in a sealed rigid cylinder. During an adiabatic process, $$100$$ $$kJ$$ of work is done on the system by a stirrer. The increase in entropy of the system is _________ $$J/K.$$

A piston-cylinder device initially contains $$0.4\,{m^3}$$ of air (to be treated as an ideal gas) at $$100$$ $$kPa$$ and $${80^ \circ }C.$$ The air is now isothermally compressed to 0.1 m3 . The work done during this process is ________ $$kJ.$$

(Take the sign convention such that work done on the system is negative)

Steam at an initial enthalpy of $$100$$ $$kJ/kg$$ and inlet velocity of $$100$$ $$m/s,$$ enters an insulated horizontal nozzle. It leaves the nozzle at $$200$$ $$m/s.$$ The exit enthalpy (in $$kJ/kg$$) is ___________