P$1.$

The above figure shows a problem, which is a modified system as shown in

the Compressed Air Energy Storage PowerPoint. A large tank with volume of

$125m^3$ is available. In this system the tank is not insulated and the

compressed air in the tank loses its energy and reduces its temperature to $293$ K

and the pressure at $10$ bar $.$ So$,$ a combustor is used to increase the temperature

to $750$ K $.$ Calculate the energy of the fuel, mass of the fuel burning natural

gas. $($Assuming all the combustion process happens at once and transfers all

the mass from the tank to the combustor, i$.$e$.m_1^{}=m_3^{}).$

Assume heating value of natural gas is $55M\frac{J}{k}g$ of fuel

$(Cp=1k\frac{J}{k}g*K)$