Question

Using an unmanned rocket to visit the space station requires 85.2 trillion BTU of energy. The best fuel for the mission will have the highest ratio of energy to volume. Based on the fuel data presented in the table, select the optimal fuel and calculate the total gallons of fuel required.
Table: Energy Output BTU/lb Density g/ml
Kerosene 18,500 0.820
Gasoline 20,900 0.737
Ethanol 11,500 0.789
Hydrogen(l) 61,100 0.0710
Which is the optimal fuel?

How many gallons of fuel are required?
Conversion units:convert energy output to BTU/gal
i need help please

Answer 1

We shall convert all of the densities to lbs/gal, so the product of
BTU/lbs and lbs/gal gives us the basis of comparison, which was "ratio of energy to volume".
grams / ml x 1 lbs/454 grams → 1 lbs/ 454 ml
1 lbs/454 ml x 3785.41 ml/gal → 3785.41 lbs/454gal
Conversion of g/ml = 8.34 lbs/gal
Looking at each fuel:

Kerosene:
18,500 x (8.34 x 0.82) = 126,517 BTU/gal

Gasoline:
20,900 x (8.34 x 0.737) = 128,463 BTU/gal

Ethanol:
11,500 x (8.34 x 0.789) = 75,673 BTU/gal

Hydrogen:
61,000 x (8.34 x 0.071) = 36,120 BTU/gal

The best fuel in terms of energy to volume ratio is Gasoline.
Gallons required:
BTU needed / BTU per gallon
= 85.2 x 10⁹ / 128,463
= 6.6 x 10⁵ gallons