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 times 10^-4 (degreeC)^-1. This canister will be filled at room temperature (23.0degreeC) and lowered deep into the Earth (where temperatures can reach 125degreeC) for storage. If the coefficient of volume expansion of the metal is 4.10 times 10^-5 (degreeC)^-1, how much waste will spill over the top if the lid becomes loose?

Explanation / Answer

from Coefficient of Cubical expansion

gamma =Y = dV/(V1 * DT)

change of VOlume dV = V1 * Y * DT1

dV = 25 * 4.1 *10^-5 * (125-23)

dV = 0.10455 gallon

VOlume expansion of Radiaactive waste

DV1 = V * Y * DT

DV1 = 25 * 9.6*10^-4 * (125-23)

DV1 = 2.448 gallon

Spill = 2.448 - 0.10455

Spill = 2.343 gallon

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