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 115°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? ______ gallons

Explanation / Answer

here,

coefficient of expansion for the metal , alpha = 9.6 * 10^-4 per degree Celsius,

and the temperature changes from 23 to 115 degrees,

we have a 92 degree temperature change

delta T = 92 degree C

and

the expansion of the canester will be , V' = 50 gal * 9.6 * 10^-4 * 92 = 4.42 gallons.

coefficient of expansion of the metal is 4.1*10^-5

so for a 92 degree temperature change the metal will expand 92 * 4.1 * 10^-5 = 3.77 * 10^-3 * the volume

then the increase in the volume of the tank will be 3.77 * 10^-3 * 50gallons = 0.1886 gallons.

the difference in the volume , V = 54.42 galons - 50.1886 gallons

V= 4.23 gallons

the waste will spill over the top of the lid is 4.23 galllons

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