Work is done on an adiabatic system due to which its velocity changes from $$10$$ $$m/s$$ to $$20$$ $$m/s,$$ elevation increases by $$20$$ $$m$$ and temperature increases by $$1$$ $$K$$. The mass of the system is $$10$$ $$kg,$$ $${{C_v} = 100J\left( {kg.K} \right)}$$ and gravitational acceleration is $$10\,\,m/{s^2}.$$ If there is no change in any other component of the energy of the system, the magnitude of total work done (in $$kJ$$) on the system is _______________.

A well insulated rigid container of volume $$1{m^3}$$ contains $$1.0$$ $$kg$$ of an ideal gas $$\left[ {{C_p} =1000\,\,\,J/\left( {kg.K} \right)} \right.$$ and $$\left. {{C_v} = 800J/\left( {kg.K} \right)} \right]$$ at a pressure of $${10^5}\,\,Pa.$$ A stirrer is rotated at constant $$rpm$$ in the container for $$1000$$ rotations and the applied torque is $$100$$ $$N$$-$$m.$$ The final temperature of the gas (in $$K$$) is _______________.

Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below:

The rate of heat loss from the turbine per $$kg$$ of steam flow rate is $$5$$ $$kW.$$ Neglecting changes in potential energy of steam, the power developed in $$kW$$ by the steam turbine per $$kg$$ of steam flow rate, is

Steam enters an adiabatic turbine operating at steady state with an enthalpy of $$3251.0kJ/kg$$ and leaves as a saturated mixture at $$15$$ $$kPa$$ with quality (dryness fraction ) $$0.9.$$ The enthalpies of the saturated liquid and vapour at $$15$$ $$kPa$$ are $${h_f} = 225.94kJ/kg$$ and $${h_g} = 2598.3kJ/kg$$ respectively. The mass flow rate of steam is $$10kg/s.$$ Kinetic and potential energy changes are negligible. The power output of the turbine in $$MW$$ is