A $4-$stroke diesel engine has a cut$-$off ratio of $1\mathrm{.}2.$ The pressure and temperature at the start of the compression process are $100$ kPa and $17C.$ The bore of the cylinder is $10$ cm and the piston stroke is $12$ cm $.$ The minimum volume of the cycle is $5\%$ of the maximum volume. Draw the P$-$v diagram and determine the power generated if the engine is running at $1600$ rpm $.$ Use variable specific heats. Also determine the mean effective pressure and thermal efficiency.

$[16]$

Note: No marks will be allotted if you use cold air standard assumption.