Explanation:
1) 1.0 ounce serving of the cereal provides 130 calories.
Then 32 ounces of breakfast cereal will provide :
= [tex]32\times 130 cal =4160 cal[/tex]
Cost of 32 ounces of cereal = $4.23
Energy from cereal with respect to dollar:
[tex]\frac{4160 cal}{\$4.23}=983.45 cal/\$[/tex]
2) Density of iso-octane = d = 0.6916 g/mL
Mass of the iso-octane = m
Volume of iso-octane = V = 1 L
[tex]m=d\times V=0.6916 g/mL\times 1L = 0.6916 g[/tex]
Moles of isooctane = [tex]\frac{0.6916 g}{114 g/mol}=0.006066 mol[/tex]
Heat of combustion of isooctane = 5450 kJ/mol
Heat released on combustion of 0.006066 moles of isooctane:
[tex]0.006066 mol\times 5450 kJ/mol=33.0633 kJ[/tex]
1 kJ = 239.006 cal
[tex]33.0633 kJ=33.0633\times 239.006 cal=7,904.23 cal[/tex]
Cost of 0.6916 g or 1 L of isooctane = $0.45
Energy from isooctane with respect to dollar:
[tex]\frac{7,904.23 cal}{\$0.45}=17,564.95 cal/\$[/tex]
We can generate large amount of energy by combustion of isooctane than the energy we getting from cereal:
17,564.95 cal/$ > 983.45 cal/$
But isooctane is an indigestible by human body so, it will be good to have cereals.
