The density of gasoline is 730 kg/m^3 at 0'C. One gallon of gasoline occupies .0038 m^3. Gasoline's volume expansion coefficient is .00096'C ^-1.
How many kilograms of gasoline are obtained when 9 gallons of gasoline are bought @ 0'C rather than 18"c (temp. at the filling station)?
answer in kg???
Multiply 9 gallons by (1 + 18C*.00096'C ^-1) That is the number of gallons you would have if the temperature were raised back to 18 C.
Next, you need to convert that number of gallons to m^3 and multiply by the density at 18 C, which that have given you in kg/m^3.
What they are really interested in, I believe, the number of EXTRA kg you get by pumping at the lower temperature.
Basically, you get 1.73% more, which comes from the 18C*.00096'C ^-1 thermal expansion term
To calculate the mass of gasoline obtained when 9 gallons are bought at 0°C instead of 18°C, we need to consider the change in volume due to the difference in temperature.
First, let's calculate the initial volume of 9 gallons of gasoline at 0°C. We know that one gallon of gasoline occupies 0.0038 m³, so 9 gallons would occupy:
9 gallons * 0.0038 m³/gallon = 0.0342 m³ (initial volume at 0°C)
Now we need to calculate the final volume at 18°C. To do this, we need to take into account the volume expansion coefficient of gasoline, which is given as 0.00096 °C⁻¹.
The change in temperature from 0°C to 18°C is:
18°C - 0°C = 18 °C
The change in volume due to temperature can be calculated as:
Change in volume = Initial volume * Volume expansion coefficient * Change in temperature
Change in volume = 0.0342 m³ * 0.00096 °C⁻¹ * 18 °C
Now, let's calculate the final volume at 18°C:
Final volume = Initial volume + Change in volume
Final volume = 0.0342 m³ + (0.0342 m³ * 0.00096 °C⁻¹ * 18 °C)
Next, we can calculate the mass of gasoline using the density of gasoline at 0°C, which is given as 730 kg/m³:
Mass of gasoline = Final volume * Density
Mass of gasoline = (0.0342 m³ + (0.0342 m³ * 0.00096 °C⁻¹ * 18 °C)) * 730 kg/m³
Now, we can calculate the final answer:
Mass of gasoline = (0.0342 m³ + (0.0342 m³ * 0.00096 °C⁻¹ * 18 °C)) * 730 kg/m³ * 9 gallons
By substituting the given values and performing the calculations, you can find the answer in kilograms.