When 1.0 grams of gasoline burns, 11500 calories of heat energy are given off. If the density of gasoline is 0.66 g/ml , how many kilocalories of energy are obtained from 1.5 gallons of gasoline?
1.5 gal * 5678ml/gal * .66g/ml * 11.5kcal/g = 64.644 kcal
g g
To solve this problem, we need to convert the units of both the density and the volume of gasoline. Let's go through the steps:
1. Convert 1.5 gallons to milliliters:
There are approximately 3.78541 liters in a gallon, so:
1.5 gallons × 3.78541 liters/gallon × 1000 ml/liter = 5678.11 ml
2. Calculate the mass of gasoline in grams:
We can use the density of gasoline to convert the volume to mass:
5678.11 ml × 0.66 g/ml = 3743.59946 g (rounded to 2 decimal places)
3. Calculate the amount of heat energy produced from 1.5 gallons of gasoline:
We know that 1 gram of gasoline produces 11500 calories of heat energy, so we can use this information to find the heat energy produced from the given mass:
3743.59946 g × (11500 calories/1 gram) = 43037994.9 calories (rounded to 1 decimal place)
4. Convert the heat energy to kilocalories:
There are 1000 calories in 1 kilocalorie, so:
43037994.9 calories ÷ 1000 = 43037.9949 kilocalories (rounded to 1 decimal place)
Therefore, approximately 43,037.9 kilocalories of energy are obtained from 1.5 gallons of gasoline.
To find out how many kilocalories of energy are obtained from 1.5 gallons of gasoline, we need to convert the volume of gasoline from gallons to grams.
First, let's convert the volume from gallons to milliliters (ml).
1 gallon is equal to 3.78541 liters, and since there are 1000 milliliters in a liter, we can calculate:
1 gallon = 3.78541 liters = 3.78541 * 1000 ml = 3785.41 ml
Now that we have the volume in milliliters, we can calculate the mass of gasoline by multiplying the volume by the density of gasoline. The density is given as 0.66 g/ml.
Mass of gasoline = volume of gasoline * density of gasoline
Mass of gasoline = 3785.41 ml * 0.66 g/ml
Mass of gasoline ≈ 2498.30 grams
Next, let's calculate the amount of energy obtained from the gasoline using the known energy output of 11500 calories per 1.0 gram of gasoline.
Energy obtained = mass of gasoline * energy output per gram
Energy obtained = 2498.30 grams * 11500 calories/gram
Energy obtained ≈ 28,732,450 calories
Finally, let's convert the energy obtained from calories to kilocalories. There are 1000 calories in 1 kilocalorie.
Energy obtained in kilocalories = Energy obtained in calories / 1000
Energy obtained in kilocalories ≈ 28,732,450 calories / 1000 ≈ 28,732.45 kilocalories
Therefore, approximately 28,732.45 kilocalories of energy are obtained from 1.5 gallons of gasoline.