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 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

25 gallons= 0.0946353 m^3

volume expansion for canister = 0.0946353 ( 4.10 x 10^-5) (132- 23) = 42.292 x 10^ -5 m^3 apprx

volume expansion for radioactive waste=  0.0946353 (9.60 x 10^-4) (132- 23)= 990.26 x 10^-5 m^3

spilled waste= 947.97 x 10^-5 m^3

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