The density of gasoline is 730 kg/m3 at 0°c. its average coefficient of volume expansion is 9.60 10-4(°c)−1. assume 1.00 gal of gasoline occupies 0.003 80 m3. how many extra kilograms of gasoline would you receive if you bought 8.50 gal of gasoline at 0°c rather than at 21.7°c from a pump that is not temperature compensated?

0.4911 kg

Explanation:

We have the following data:

is the density of gasoline at

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:

(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 :

(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

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