Answer: 0.4911 kg
Explanation:
We have the following data:
is the density of gasoline at ![0\°C](https://tex.z-dn.net/?f=0%5C%C2%B0C)
is the average coefficient of volume expansion
We need to find the extra kilograms of gasoline.
So, firstly we need to transform the volume of gasoline from gallons to
:
(1)
Knowing density is given by:
, we can find the mass
of 8.50 gallons:
![m_{1}=\rho_{0\°C}V](https://tex.z-dn.net/?f=m_%7B1%7D%3D%5Crho_%7B0%5C%C2%B0C%7DV)
(2)
Now, we have to calculate the factor
by which the volume of gasoline is increased with the temperature, which is given by:
(3)
Where
is the initial temperature and
is the final temperature.
(4)
(5)
With this, we can calculate the density of gasoline at
:
![\rho_{21.7\°C}=730 kg/m^{3} f=(730 kg/m^{3})(1.020832)](https://tex.z-dn.net/?f=%5Crho_%7B21.7%5C%C2%B0C%7D%3D730%20kg%2Fm%5E%7B3%7D%20f%3D%28730%20kg%2Fm%5E%7B3%7D%29%281.020832%29)
(6)
Now we can calculate the mass of gasoline at this temperature:
(7)
(8)
(9)
And finally calculate the mass difference
:
(10)
(11) This is the extra mass of gasoline