$2.(25$ points$)$

An ideal Otto cycle has a compression ratio of $10.$ At the beginning of the compression process the working fluid, air, is at $150$ kPa and $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Heat is transferred at $\backslash (110\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$hr$\}\backslash )$ during a constant volume heat addition process and the mass flow rate of air in the cycle is $\backslash (0\mathrm{.}125\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$hr$\}\backslash ).$ Assume the heat capacity of air is a function of temperature.

a$)(5$ points$)$ sketch a PV diagram of the cycle and for each process indicate the direction of heat or work flow

b$)$ determine the pressure and temperature at the end of the heat addition process

c$)$ determine the net work output in KW

d$)$ determine the thermal efficiency of the process