A steel billet of $$2000$$ $$kg$$ mass is to be cooled from $$1250$$ $$K$$ to $$450$$ $$K.$$ The heat released during this process is to be used as a source of energy. The ambient temperature is $$303$$ $$K$$ and specific heat of steel is $$0.5$$ $$kJ/kg K.$$ the available energy of this billet is

A heat reservoir at $$900$$ $$K$$ is brought into contact with the ambient at $$300$$ $$K$$ for a short time. During this period $$9000$$ $$kJ$$ of heat is lost by the heat reservoir. The total loss in availability due to this process is