The storage of radioactive waste is an important problem in the nuclear industry

Question

The storage of radioactive waste is an important problem in the nuclear industry. One problem that scientists must take into account is volumetric expansion. Consider a 25.0-gallon metal canister of diameter 22.0 inches filled with a radioactive waste possessing a coefficient of volume expansion of 9.60 × 10-4 (°C)–1. This canister will be filled at room temperature (23.0°C) and lowered deep into the Earth (where temperatures can reach 145°C) for storage. If the coefficient of volume expansion of the metal is 4.10 × 10-5 (°C)–1, how much waste will spill over the top if the lid becomes loose?

Explanation / Answer

we originally have 25 gallons of junk. If the coefficient of expansion for the gunk is 9.6 x 10^-4 per degree Celsius, and the temperature changes from 23 to 145 degrees, we have a 122 degree temperature change and the expansion of the junk will be 25 gal x 9.6 x 10^-4 x 122 = 2.93 gallons.

The coefficient of expansion of the metal is 4.1x10^-5
so for a 122 degree temperature change the metal will expand 122 x 4.1 x 10^-5 x volume

= 5 x 10^-3 x 25 = 125 x 10^-3 gallons

the difference in the volume of the junk (which is now 25 + 2.93 ) = 27.93 gallons and the tank which is (25 +0.125) = 25.125 gallons is the amount of junk which will overflow. That's 27.93 - 25.125 gallons = 2.805 gallons.

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