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 142°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

chance in volume = c*| Tf - Ti|*Vo
For the canister,increase in volume= 4.10 x 10-5 * |142 - 23|*50 = 0.24395 gal.
For the waste , increase in volume = 9.60 × 10-4 * |142- 23|*50 = 5.712 gal.

So, how much extra waste spills out=5.712-0.24395 = 5.46805 gal

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