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 50.0-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 132°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 50 gallons of gunk. If the coefficient of expansion for the gunk is 9.6 x 10^-4 per degree Celsius, and the temperature changes from 23 to 155 degrees, we have a 109 degree temperature change and the expansion of the gunk will be 50 gal x 9.6 x 10^-4 x 109 = 5.235 gallons.

The coefficient of expansion of the metal is 4.1x10^-5
so for a 109 degree temperature change the metal will expand 109 x 4.1 x 10^-5 = 4.469 x 10^-3 x the volume. The increase in the volume of the tank will be 4.469 x 10^-3 x 50gallons = 0.223 gallons. the difference in the volume of the gunk (which is now 50 + 5.235 ) =55.235 gallons and the tank which is (50 +0.223) = 50.223 gallons is the amount of gunk which will overflow. That's 55.235 - 50.223 gallons = 5.012 gallons

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