A steam turbine receives steam steadily at $$10$$ $$bar$$ with an enthalpy of $$3000$$ $$kJ/kg$$ and discharges at $$1$$ bar with an enthalpy of $$2700$$ $$kJ/kg.$$ The work output is $$250$$ $$kJ/kg.$$ The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundings is equal to

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

The first law of thermodynamics takes the form $$W = - \Delta \,H$$ when applied to :