Final answer:
The Calorie content of one serving of breakfast cereal with 3 g of protein, 18 g of carbohydrates, and 6 g of fat is 140.7 Calories. The energy density and cost-effectiveness of cereal versus isooctane would require further information on the heat produced by the combustion of isooctane to complete the comparison.
Step-by-step explanation:
To calculate the Calorie content of a serving of breakfast cereal, we'll use the given information. We know that proteins and carbohydrates both have an average of 4.1 Calories per gram, while fat has 9.1 Calories per gram. The cereal contains 3 g of protein, 18 g of carbohydrates, and 6 g of fat per serving. Therefore, the total Calorie content is:
- (3 g of protein x 4.1 Calories/g) + (18 g of carbohydrates x 4.1 Calories/g) + (6 g of fat x 9.1 Calories/g)
- (3 x 4.1) + (18 x 4.1) + (6 x 9.1)
- 12.3 Calories from protein + 73.8 Calories from carbohydrates + 54.6 Calories from fat
- Total = 140.7 Calories per serving
For the energy density comparison between cereal and isooctane, we'll have to consider the cost per energy unit. A 32-ounce box of breakfast cereal provides 130 Calories per 1-ounce serving and costs $4.23. In kilojoules (since 1 Calorie is approximately 4.184 kilojoules), that's 130 x 4.184 kJ/ounce. Isooctane's energy content can be calculated through its combustion under standard conditions. The density and price are given to determine which source is cheaper per energy unit.