my teacher wasn't in school and this assignment is due @ 7am!!!!!
The density of gasoline is 730 kg per cubic meter. One gallon of gasoline occupies .0038 cubic meters. Gasoline's volume expansion coefficient is .00096` C (^-1).
How many extra kilograms of gasoline are obtained when 9 gallons of gasoline are bought at 0` C rather than at 18` C (temp. at the filling station) ?
answer should be in kg???
To calculate the extra kilograms of gasoline obtained when 9 gallons are bought at 0` C rather than at 18` C, we can follow these steps:
Step 1: Calculate the initial volume of gasoline at 0` C:
Since 1 gallon of gasoline occupies 0.0038 cubic meters, the initial volume of 9 gallons at 0` C will be:
9 gallons * 0.0038 cubic meters per gallon = 0.0342 cubic meters.
Step 2: Calculate the temperature difference:
The temperature difference between 0` C and 18` C is:
18` C - 0` C = 18` C.
Step 3: Calculate the volume expansion of gasoline:
The volume expansion coefficient of gasoline is 0.00096` C (^-1).
Therefore, the volume expansion will be:
0.00096` C (^-1) * 0.0342 cubic meters * 18` C = 0.00058738 cubic meters.
Step 4: Calculate the final volume of gasoline at 18` C:
The final volume at 18` C will be the initial volume plus the volume expansion:
0.0342 cubic meters + 0.00058738 cubic meters = 0.03478738 cubic meters.
Step 5: Calculate the extra kilograms of gasoline obtained:
The density of gasoline is 730 kg per cubic meter.
Therefore, the extra kilograms of gasoline obtained will be the difference in volume multiplied by the density:
(0.03478738 cubic meters - 0.0342 cubic meters) * 730 kg per cubic meter = 0.00058738 cubic meters * 730 kg per cubic meter = 0.428 kg (rounded to three decimal places).
Therefore, when 9 gallons of gasoline are bought at 0` C rather than at 18` C, you would obtain approximately 0.428 kilograms of extra gasoline.
To calculate the extra kilograms of gasoline obtained when buying 9 gallons of gasoline at different temperatures, you need to consider the change in volume due to temperature and the density of gasoline.
Here's how you can find the answer:
1. Convert gallons to cubic meters:
- 9 gallons * 0.0038 cubic meters/gallon = 0.0342 cubic meters
2. Calculate the change in volume due to temperature:
- Given temperature difference: 18`C - 0`C = 18`C
- Volume expansion coefficient: 0.00096` C (^-1)
- Change in volume = Volume * Expansion coefficient * Temperature change
- Change in volume = 0.0342 cubic meters * 0.00096` C (^-1) * 18`C = 0.000586176 cubic meters
3. Calculate the extra kilograms of gasoline:
- Density of gasoline: 730 kg per cubic meter
- Extra kilograms = Change in volume * Density
- Extra kilograms = 0.000586176 cubic meters * 730 kg per cubic meter = 0.4276 kg
Therefore, when buying 9 gallons of gasoline at 0`C instead of 18`C, you would obtain an extra 0.4276 kilograms of gasoline.