H$7-4$: An ideal air$-$standard power cycle is shown below. The mass of the air is $10$kg$.$ Some of the properties of the air at each state are given in the table. The cycle has the following processes: process $12$: isentropic compression; process $23$: constant$-$volume heat addition; process $34$: isentropic expansion; process $41$: constant$-$volume heat rejection. Heat transfer to the cycle is from a high$-$temperature reservoir at a temperature of $1200$C during process $23,$ and heat transfer from the cycle is to a low$-$temperature reservoir at a temperature of $20$C during process $41.$ Determine $($a$)$ the thermal efficiency of the cycle; $($b$)$ the entropy generation for the whole cycle; $($c$)$ if the cycle violates the second law of thermodynamics by using both Carnot$$s principles and the increase of entropy principle. Answers: $($a$)52\%$; $($b$)7\mathrm{.}6$ kJ$/$K; $($c$)$ use both Carnot$$s principles and the increase of entropy principle. Hints: $1.$ The power cycle is NOT a cold air$-$standard cycle; $2.$ You do NOT have to use all the provided properties.

State u $($kJ$/$kg$)$ h $($kJ$/$kg$)1206\mathrm{.}8290\mathrm{.}02474\mathrm{.}9662\mathrm{.}231273\mathrm{.}01726\mathrm{.}04588\mathrm{.}4816\mathrm{.}8$