e storage of radioactive waste is an important problem in the nuclear industry.

Question

e storage of radioactive waste is an important problem in the nuclear industry. One problem that scientists st take into account is volumetric expansion. Consider a 40.0-gallon metal canister of diameter 22.0 inches filled with a radioactive waste possessing a coefficient of volume expansion of 9.60 x 104 (oc) 1. This canister will be filled at room temperature (23.0°C) and lowered deep into the Earth (where temperatures can reach 138°C) for storage. If the coefficient of volume expansion of the metal is 4.10 x105 (OC) 1, how much waste will spill over the top if the lid becomes loose? Number 4.416 gallons

Explanation / Answer

the equation for volume spilled wil be:

Vspilled = Vcont*( Tearth - Troom )*( krad - kmetal )

where Vcont = volume of container = 40 gallon

Tearth =Earth's temp. = 138 0C

Troom = room's temp. = 23 0C

krad = cofficient of volume expansion of the radioactive waste filled in container = 9.60*10-4  0C-1

kmetal = cofficient of volume expansion of metal = 4.10 *10-5

by putting all the values in this eq.

Vspilled = Vcont*( Tearth - Troom )*( krad - kmetal )

= 40*(138 - 23)* ( 9.60*10-4 - 4.10*10-5 )

= 4.2274 gallons

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