Physics - Volume Expansion

Question

The average coefficient of volume expansion for carbon tetrachloride is 5.81 multiplied by 10-4 (°C)-1. If a 54.5 gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C, how much will spill over when the temperature rises to 30.0°C?

I used the volume expansion equation and got 0.633 but that is supposedly not the right answer. Does anyone know what is wrong?

Answer 1

Your working equation is

V = Vo[1 + (alpha)(delta T)]

where

V = volume of susbstance at any T

Vo = volume of substance start = 54.5 gal.

alpha = coefficient of volume expansion = 5.81 x 10^-4

delta T = 30 - 10 = 20

Substituting appropriate values,

V = 54.5[1 + (5.81 x 10^-4)(20)]

V = 55.133 gals.

Excess volume = 55.133 - 54.5 = 0.633

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I believe your solution and mine are correct. Unless somebody else can come up with a different solution, then I will maintain that the answer to the problem is 0.633 gal.

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From the tables of physical constants, the coefficient of volumetric expansions for carbon tetrachloride is given as 1.236 x 10^-3

If this is the coefficient of volumetric expansion that will be used then, the excess volume (volume that will spill),

54.5 [1 + (1.236 x 10^-3)(20)] - 54.5 = 1.347 gal.

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Anyway, the solution to this problem still follows the basic formula of

Vol spill = 54.5[1 + (alpha)(20)] - 54.5

and the only way that there will be a different answer for the spilled volume is when a different value of alpha is used.

Answer 2

54.5 gal x 5.81e-4/C x 20 = 0.633

so I agree with you.

Perhaps you have to consider the expansion of the steel container? But you need to know the shape to do that calculation.

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