Coefficient of volume and linear expansion question.?

Question

Hi, working through a homework problem but I can't seem to get the answer to this one:

A steel gas tank of volume 0.0700 meters cubed is filled to the top with gasoline at 20 degrees celsius. The tank is placed inside a chamber with an interior temperature of 50 degrees celsius. The coefficient of linear expansion of steel is 12.0*10^-6 and the coefficient of volume expansion for gasoline is 9.50*10^-4 After the tank and its contents reach thermal equilibrium with the interior of the chamber, how much gasoline has spilled?

Any explanation of how to do this problem would be greatly appreciated!

Answer 1

If the gasoline is filled to the top, then the volume of the gasoline is also 0.0700 mters cubed

Always remember that the coefficient of volume expansion is 3 times its coefficient of linear expansion... so the coefficient of volume expansion of steel is 36.0*10^-6

Okay... now let us get the expansion of the steel tank...
change in volume for steel = (coefficient of volume expansion)(original volume)(change in temperature)
= (36.0*10^-6 /C) (0.0700 meters cubed) (50 C - 30 C)
= 5.04*10^-5 meters cubed

And now the expansion of the gasoline...
change in volume of gasoline = (coefficient of volume expansion) (original volume) (change in temperature)
= (9.50*10^-4/C) (0.0700 meters cubed) (50 C - 30 C)
= 1.33*10^-3 meters cubed

Okay, now we get the volume of the gasoline spilled...
(1.33*10^-3 meters cubed) - (5.04*10^-5 meters cubed)
=1. 2896^-3 meters cubed

Answer 2

Coefficient Expansion Steel

Answer 3

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RE:
Coefficient of volume and linear expansion question.?
Hi, working through a homework problem but I can't seem to get the answer to this one:

A steel gas tank of volume 0.0700 meters cubed is filled to the top with gasoline at 20 degrees celsius. The tank is placed inside a chamber with an interior temperature of 50 degrees celsius. The...

Answer 4

well first you have to calculate the length of one side of the steel can and then use the linear expansion coefficient to find the final length of the side of the steel tank remember all four side and maybe the bottom as well and then use the volume coefficient for the gas and find the final volume of the gas the difference between the volume of gas and the volume of tank will spill if the volume of gas is bigger than the volume of tank remember the volume of gas and tank start the same and to get the length of the side for a cube length of side to the third power is the volume so just do the reverse of it to get the length.