An air$-$standard Dual Cycle operates with a compression ratio of $14.$ The conditions at the beginning of compression are $100$ kPa and $300$ K $.$ The maximum temperature in the cycle is $2200$ K and the heat added at constant volume is twice the heat added at constant pressure

a$.$ Draw the cycle on a P$-$v diagram.

b$.$ Draw the cycle on a T$-$s diagram.

c$.$ Calculate the pressure, temperature, and specific volume at each corner of the cycls

d$.$ Calculate the thermal efficiency of the cycle.

e$.$ Calculate the mean effective pressure.

Note: $C_p=1\mathrm{.}005k\frac{J}{k}gK,C_v=0\mathrm{.}718k\frac{J}{k}gK,R=0\mathrm{.}287k\frac{J}{k}gK,k=1\mathrm{.}4$