I apologize if I\'m asking this question in the wrong area. I\'m new to this sit

Question

I apologize if I'm asking this question in the wrong area. I'm new to this site and was studying this particular problem, ran into a hurdle, clicked the "More Help for this Problem" button, and this is where it sent me.

Here's the problem:

The average coefficient of volume expansion for carbon tetrachloride is 5.81E-4/Celcius. Ifa 50.0-gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0 degrees celcius, how much will spill over when the temperature rises to 30.0 degrees celcius?

Here is the solution as it is worked out on cramster.com:

Coefficient of volume expansion of carbon tetrachloride =5.81E-4 / degrees celcius
Initial volume V = 50gal

Volume expansion of carbon tetrachloride
                   v = V t t=Increase in temperature
                       = (50 x 5.81E-4 x 20) gal                     = (30 - 10) degrees celcius
                       = 0.581 gal                                         = 20 degrees celcius

Coefficient of volume expansion of stell
                   s = 3 x 11E-6 / degrees celcius

Volume expansion of the steel container
                   Vs = V s t
                         = (50 x 3 x 11E-6 x 20) gal
                         = 0.033 gal

Carbon tetrachloride spills over
                         = V = Vs
                         = (0.581 - 0.033) gal
                         = 0.548 gal

Everything on here makes sense to me except for the coefficient of volume expansion of steel: s = 3 x 11E-6 / degrees celcius. The book clearly states that this value is "11E-6 / degrees celcius" (Link - if you want to see the page - pg. 506 - http://books.google.com/books?id=1DZz341Pp50C&pg=PR24&lpg=PR24&dq=principles+of+physics+4th+edition+online&source=bl&ots=Rkx0oEFLqp&sig=okzpcL0ZJjlb3dgTYY9c573XAu4&hl=en&sa=X&ei=ParpTuvYHMjC2wXjovihCA&ved=0CEUQ6AEwAg#v=onepage&q=principles%20of%20physics%204th%20edition%20online&f=false) Where is the "3" coming from? Why did they solve this problem by multiplying the coefficient of volume expansion of steel by "3"?

Explanation / Answer

We calculate the volume expansion of some x gal of carbon tetrachloride from 10 degree celsius to 30 dehree celsius at the uniform increase of 5.81 x 10^-4 per degree (celsiu degree) and at 30 degree celsius that x gallon at 10 degree celsius has expanded and occupied 50 gallon container fully.

Then the difference 50-x is spill, had we heated 50 gal of c terachloride.

Let x be the volume of the carbon tetrachloride at 10 degree, which, when heated to 30 degree celsius, occupies 50 gal cotainer fully.

Therefore the expansion of x volume of the gas when heated from 10 to 30 degree celsius = x*coefficient of expansion*increase in temperature. = x*5.81*10^(-4)*20.

Therefore at 30 degree the total volume of carbon tetra chloride in the steel container = x+x*5.81*10^(-4)20 = 50 gallons.

Therefore, (1+0.01162)x= 50. Or

x = 50/1.01162 = 49.42567367 gal.

Therefore the spill = (50 - 49.42567367 ) gal = 0.574326328 gal is quantum of spill had we heated 50 gal gas full in the container from 10 degree to 30 degree.

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