An adiabatic steam turbine receives dry saturated steam at $$1.0\,\,\,MN/{m^2}$$ and discharges it $$0.1\,\,\,MN/{m^2}.$$ The steam flow rate is $$3$$ $$kg/s$$ and the moisture at exit in negligible. If the ambient temperature is $$300$$ $$K,$$ determine the rate of entropy production and the lost power.

A steel ball of mass $$1$$ $$kg$$ and specific heat $$0.4$$ $$kJ/kg$$ is at temperature of $${60^ \circ }C.$$ It is dropped into $$1$$ $$kg$$ water at $${20^ \circ }C.$$ The final steady state temperature of water is