One side of a wall is maintained at $$400K$$ and the other at $$300K.$$ The rate of heat transfer through the wall is $$1000W$$ and the surrounding temperature is $${25^ \circ }C.$$ Assuming no generation of heat within the wall, the irreversibility (in $$W$$) due to heat transfer through the wall is ____________

The pressure, temperature and velocity of air flowing in a pipe are $$5$$ $$bar,$$ $$500$$ $$K$$ and $$50$$ $$m/s,$$ respectively. The specific heats of air at constant pressure and at constant volume are $$1.005kJ/kgK$$ and $$0.718$$ $$kJ/kgK,$$ respectively. Neglect potential energy. If the pressure and temperature of the surroundings are $$1$$ bar and $$300$$ $$K,$$ respectively, the available energy in $$kJ/kg$$ of the air stream is

$$A$$ gas expands in a frictionless piston-cylinder arrangement. The expansion process is very slow, and is resisted by an ambient pressure of $$100kPa.$$ During the expansion process, the pressure of the system (gas) remains constant at $$300$$ $$kPa.$$ The change in volume of the gas is $$0.01{m^3}.$$

The maximum amount of work that could be utilized from the above process is

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