Consider a spark$-$ignition engine with a compression ratio of $8.$ At the beginning of the compression step, air is at $90$kPa and $298\mathrm{.}15K.$ In the heat addition step, $800k\frac{J}{k}g$ of heat is supplied. For this engine, calculate:

a$.$ the temperature and pressure at each state of the process

b$.$ the net specific work for the cycle

c$.$ the thermal efficiency of the engine

A complete solution should include a labeled diagram of each state. The gas constant $R$ for air is $0\mathrm{.}2870k\frac{J}{k}g*K,$ and take the specific heat capacities to be $c_P=1\mathrm{.}005k\frac{J}{k}g*K$ and $c_v=0\mathrm{.}718k\frac{J}{k}g*K.$

Selected Ans: $W_{\text{n}\text{e}\text{t}}=-451\mathrm{.}6k\frac{J}{k}g,{}_{th}=56\mathrm{.}4\%$