Air enters a frictionless adiabatic converging nozzle at $$10$$ bar, $$500$$ $$K$$ with negligible velocity. The nozzle dis-charges to a region at $$2$$ bar. If the exit area of the nozzle is $$2.5\,c{m^2}$$ find the flow rate of air through the nozzle. Assume for air, $${C_p} = 1005\,J/kg\,K$$ and $${C_v} = 718\,J/kg\,K.$$

For an ideal gas the expression $$\left[ {T{{\left( {{{\delta s} \over {\delta T}}} \right)}_p} - T{{\left( {{{\delta s} \over {\delta T}}} \right)}_v}} \right]$$ is always equal to :

A system undergoes a state change from $$1$$ to $$2.$$ According to the second law of thermodynamics, for the process to be feasible, the entropy changes, $${S_2} - {S_1}$$ of the system

At a place where the surroundings are at $$1$$ bar $${27^ \circ }C,$$ a closed rigid thermally insulated tank contains $$2$$ $$kg$$ air at $$2$$ bar, $${27^ \circ }C,$$ This air is then churned for a while, by a paddle wheel connected to an external motor. If it is given that the irreversibility of the process is $$100$$ $$kJ,$$ find the final temperature and the increase in availability of air. Assume for air $${C_v} = 0.718\,\,kJ/kg\,K$$