0 . 3g of ethane undergoes combustion at 27 ° C in a bomb...

The bomb calorimeter is an instrument used to measure the heat of reaction at a fixed volume and the measured heat which is called the change of internal energy.
By combustion of $1$ mole

${C}_{2}{H}_{6} ( \Delta U ) = - \dfrac{Heatcapacity \times ∆ T}{mass} \times Molarmass = - \dfrac{20 \times 0 . 5}{0 . 3} \times 30 = - 1000kJ$

${C}_{2}{H}_{6} ( g ) + 7 / 2{O}_{2} ( g ) \to 2{CO}_{2} ( g ) + 3{H}_{2}O ( l )$

$\Deltang = 2 - ( 2 + 7 / 2 ) = - ( 7 / 2 )$

$\Delta H = \Delta U + \Delta nRT$

$= - 1000 - 7 / 2 \times 8 . 3 \times 300kJ$

$= - 1000 - 6 . 225$

$= - 1006kJ$

So heat released $= 1006kJ{mol}^{- 1}$