Question

A solid brass sphere is subjected to a pressure of 1.00 105 Pa due to the earth's atmosphere. On Venus the pressure due to the atmosphere is 9.00 106 Pa. By what fraction ?r/r0 (including the algebraic sign) does the radius of the sphere change when it is exposed to the Venusian atmosphere? Assume that the change in radius is very small relative to the initial radius. ?r r0 =

Answer 1

We know that change in pressure needed to change volume by dV is given by:

dP = -B(dV/V0)

B = Bulk modulus

for brass value of B = 6.7*10^10 Pa

Now given that

dP = P_Venus - P_earth

dP = 9*10^6 Pa - 1*10^5 = 90*10^5 - 1*10^5 = 89*10^5 Pa

So,

dV/V0 = -dP/B = -89*10^5/(6.7*10^10)

dV/V0 = -13.3*10^-5

Now Volume is given by:

V0 = 4*pi*r0^3/3

dV = 4*pi*3*r0^2*dr/3 = 4*pi*r0^2*dr

So,

dV/V0 = 4*pi*r0^2*dr/(4*pi*r0^3/3)

dV/V0 = 3*dr/r0

dr/r0 = (1/3)*(dV/V0)

dr/r0 = (1/3)*(-13.3*10^-5) = -4.43*10^-5

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