A steel beam is to be installed on a spacecraft. By what percentage will its volume increase when placed in a vacuum? You may assume that the temperature remains the same and that the bulk modulus of steel is 6.0x1010 N m-2.
A)1.7x10-6 %.
B)1.7x10-8 %.
C)1.7x10-5 %.
D)1.7x10-4 %.
E)1.7x10-3 %.

Question

Quizplus · Accepted Answer

According to the formula for bulk modulus, B = -V(dP/dV). 
Since the temperature remains the same, we can assume that the initial pressure and final pressure are the same (i.e. atmospheric pressure). 
Thus, -V(dP/dV) = B. 
When the beam is placed in a vacuum, the external pressure is reduced to zero. 
So, the new bulk modulus, B', can be given by B' = -V(dP'/dV) = 0. 
From the above equations, we get (dV/V) = -(B'-B)/B = (6.0x10^10 N m^-2)/6.0x10^10 N m^-2 = 1.7x10^-8. 
Therefore, the percentage increase in volume is (dV/V)x100 = 1.7x10^-8 x 100 = 1.7x10^-6%. 
Hence, the best choice is B, which gives the correct percentage increase in volume of the steel beam in a vacuum.

A Steel Beam Is to Be Installed on a Spacecraft