A four$-$stroke cycle gas engine has a bore of $20$ cm and a stroke of $40$ cm $.$ The

compression ratio is $6.$ In a test on the engine the indicated mean effective pressure is

$5$ bar, the air to gas ratio is $6$:$1,$ and the calorific value of the gas is $12M\frac{J}{m}3$ at NTP$.$

At the beginning of the compression stroke the temperature is $77C$ and pressure is

$0\mathrm{.}98$ bar. Neglecting residual gases, determine the indicated power, the thermal

efficiency and the relative efficiency of the engine at $250$ rpm $.$