A piece of aluminum (bulk modulus 7.1 x 1010 N/m2) is placed in a vacuum chamber where the air pressure is 0.307 x 105 Pa. The vacuum pump is then turned on and the pressure is further reduced to zero. Determine the fractional change V/V0 in the volume of the aluminum.
To determine the fractional change in volume of the aluminum, we can use the equation that relates the bulk modulus (K) with the change in pressure (ΔP) and the fractional change in volume (ΔV/V0):
ΔP = -K * (ΔV/V0)
Where:
ΔP = change in pressure
K = bulk modulus
ΔV = change in volume
V0 = initial volume
In this case, the initial pressure is 0.307 x 10^5 Pa and the final pressure is 0 Pa, which corresponds to a change in pressure (ΔP) of -0.307 x 10^5 Pa.
We need to solve for ΔV/V0. Rearranging the equation, we have:
ΔV/V0 = - ΔP / K
Substituting the values, we have:
ΔV/V0 = -(-0.307 x 10^5 Pa) / (7.1 x 10^10 N/m^2)
Simplifying the expression, we get:
ΔV/V0 ≈ 4.32 x 10^-16
Therefore, the fractional change in the volume of the aluminum is approximately 4.32 x 10^-16.