An aeroplane weighing 63000 kg flies up from sea level to a height of ...
Calculation of Fuel Cost for Flight
Given Data:
- Weight of the aeroplane = 63000 kg
- Height to which it flies = 8000 m
- Efficiency of the engine = 30%
- Selling price of octane = Rs 3/l
- Density of octane = 0.705 g/ml
- Heat of combustion of octane = 1300 Kcal/mol
Calculation of Fuel Consumption:
The potential energy gained by the aeroplane on reaching a height of 8000 m can be calculated as:
Potential Energy = mgh
where m = mass of the aeroplane, g = acceleration due to gravity, and h = height
On substituting the given values, we get:
Potential Energy = 63000 x 9.8 x 8000
= 4.94 x 10^9 J
The actual energy required by the aeroplane can be calculated using the efficiency of the engine:
Actual Energy = Potential Energy / Efficiency
= 4.94 x 10^9 / 0.3
= 1.65 x 10^10 J
The number of moles of octane required to produce this energy can be calculated using the heat of combustion:
Number of Moles = Actual Energy / Heat of Combustion
= 1.65 x 10^10 / (1300 x 1000)
= 12.69 mol
The mass of octane required can be calculated using the density of octane:
Mass = Number of Moles x Molar Mass x Density
where Molar Mass of octane = 114.23 g/mol
On substituting the given values, we get:
Mass = 12.69 x 114.23 x 0.705
= 1004.38 g
The fuel cost can be calculated using the selling price of octane:
Fuel Cost = Mass x Selling Price / 1000
= 1004.38 x 3 / 1000
= Rs 3.01
Conclusion:
Thus, the fuel cost for the given flight is Rs 3.01.