Two compressible solids are formed into spheres of the same size.The bulk modulus of sphere two is twice as large as the bulk modulus of sphere one.You now increase the pressure on both spheres by the same amount.As a result of the increased pressure,how is the change in volume of sphere two (△V₂)related to the change in volume of sphere one (V₁)? A) ΔV₂=2ΔV₁ B) ΔV₂= 4ΔV₁ C) ΔV₂=ΔV₁ D) ΔV₂= 1/2ΔV₁ E) ΔV₂= 1/4ΔV₁

Question

Quizplus · Accepted Answer

The change in volume of a sphere is related to its bulk modulus and the increase in pressure by the following equation: ΔV = -V (ΔP/B). Since the spheres have the same size, their initial volumes are the same, and we can compare the changes in volume directly. Since the bulk modulus of sphere two is twice as large as the bulk modulus of sphere one, its change in volume will be half as much as sphere one's change in volume. Therefore, ΔVS2/B2 = (1/2) ΔVS1/B1. Rearranging this equation gives ΔVS2 = (B2/B1) (1/2) ΔVS1, or ΔVS2 = (1/2) ΔVS1 (since B2 = 2B1). Therefore, the change in volume of sphere two is half as much as the change in volume of sphere one, or ΔVS2 = 1/2 ΔVS1.

Two Compressible Solids Are Formed into Spheres of the Same