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 (ΔV₁)? A) ΔV₂=2ΔV₁ B) ΔV₂= 4ΔV₁ C) vV₂=ΔV₁ D) ΔV₂= 1/2ΔV₁ E) ΔV₂= 1/4ΔV₁

Question

Quizplus · Accepted Answer

The change in volume of a sphere under pressure is given by ΔV = -V(ΔP)/B, where B is the bulk modulus of the sphere. Since sphere two has twice the bulk modulus of sphere one, it will experience half the change in volume for the same change in pressure. Therefore, ΔVS2/B2 = 1/2(ΔVS1/B1). Dividing both sides by the initial volume of sphere two, V2, gives ΔVS2/V2B2 = 1/2ΔVS1/V1B1. Simplifying this expression gives ΔVS2/V2 = 1/2ΔVS1/V1, which means that the change in volume of sphere two is related to the change in volume of sphere one by a factor of 1/2. Therefore, choice D is the correct answer.

Two Compressible Solids Are Formed into Spheres of the Same