Thermal expansion of tank and contents.

[caperjay]

Homework Statement

At 5°c, a steel tank is 6m high, 9m in diameter, and contains oil to the 5.9m level. A heating coil is put into service, causing 3.4m^3 of oil to spill over the top of the tank by the time the final temperature is reached. Calculate the final temperature, if the coefficient of expansion of the oil is 0.00041, and coefficient of expansion for steel is 0.0000165. Note: Do not neglect the expansion of the tank.

Homework Equations

Equation for volumetric expansion for solids. ΔV= V x 3∂ x ΔT
Equation for volumetric expansion fo liquids. ΔV= V x β x ΔT
V= volume ∂=coefficient of expansion, ΔT=change in temperature, β= coefficient of expansion liquid.


3. attempt

I've been working on this one for a while now, having a hard time developing a formula that takes expansion of both into consideration. I've tried solving them seperatly, and I tried using a ratio to solove the problem, but I can't get anything close to the answer, which is 74.9°c.

If someone could just get me onto the right track, i'd like to solve it myself, thanks.

 

[gnulinger]

How are you calculating the final volume of the container? Are you are using the equation for volumetric expansion of solids? I'm not sure that's right, because the container is hollow. So rather than figuring out the change in volume of a solid steel tank, try to find the change in volume of a container made up of sheets of steel.

 

[caperjay]

Yes that formula works for solids, as well as hollow vessels. I've used it to solve similar problems. This one is just a bit harder since there's two unknowns, the final temperature, and the change in volume. I know that the oil will expand a lot more than the vessel will, and that the oil starts off with 6.36m^3 less that the size of the tank.
I've also figured out that if the tank didn't expand that the oil would need to increase by 9.76m^3 to spill 3.4m^3, and that a final temperature of 68.37°c, would be required to achieve this.

I am just having trouble including the expansion of the vessel, or deriving a formula for this.

Thanks in advance.

Jay

 

[JaimeR]

I would love to see the answer to this question! i am stuck on it as well, 3rd's...urgh i have found a few questions in the book that throws a curve ball. I am absolutley stuck as to how to solve this with 2 unknowns, volume and temperature of the steel tank and oil. i have got to the same numbers as above but can not get the right one. maybe they made a typo...found a couple so far.
Thanks
Jaime
I need some serious help...can't let it go!

 

[gneill]

I would love to see the answer to this question! i am stuck on it as well, 3rd's...urgh i have found a few questions in the book that throws a curve ball. I am absolutley stuck as to how to solve this with 2 unknowns, volume and temperature of the steel tank and oil. i have got to the same numbers as above but can not get the right one. maybe they made a typo...found a couple so far.
Thanks
Jaime
I need some serious help...can't let it go!

Show what you've tried so that we can see how to help.

 

[caperjay]

I would love to see the answer to this question! i am stuck on it as well, 3rd's...urgh i have found a few questions in the book that throws a curve ball. I am absolutley stuck as to how to solve this with 2 unknowns, volume and temperature of the steel tank and oil. i have got to the same numbers as above but can not get the right one. maybe they made a typo...found a couple so far.
Thanks
Jaime
I need some serious help...can't let it go!

Hey Jaime,

I've since solved that problem, and from what I've been told from guys at work its more of a 2nd class problem, but anyways, here's how I solved it.

Vtank + ΔVtank = Voil + ΔVoil - 3.4

381.7 + 381.7x3x0.0000012(T-5) = 375.15 + 375.15x0.00041(T-5) - 3.4

From here you just equate the problem and solve for T.