#volume decrease

A silver sphere of radius 8cm at 70∘C is cooled to 20∘C. What is the decrease in its volume? (αl\=1.9×10−5K−1)

Given: r = 8cm, V0 = 43π×83 = 20483πcm3, ΔT = 20−70 = −50∘C, αl = 1.9×10−5K−1. αv = 3αl = 3×1.9×10−5 = 5.7×10−5K−1. ΔV = V0αvΔT = 20483π×5.7×10−5×(−50). ΔV = 20483π×(−2.85×10−3)≈−6.12π≈−19.22cm3 (decrease of 19.22cm3).

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.