Problem L $(15$ pts$)$ An engine operates on an ideal Diesel cycle which has a compression ratio of $16.$ Al the beginning of the isentropic compression process, the pressure is $100$ kPa and the temperature $1is22C.$ The maximum temperature in the cycle is $1800$ K $.$ Calculate:

a$)$ The cut$-$off ratio,

b$)$ The cycle thermal officiency,

c$)$ The mean effective pressure, and

d$)$ The exergy destroyed per unit mass for the cycle.

Note: To get full credit, you need to assume air ideal gas with variable specific heats