A 200 MPa pressure is applied to a copper sphere with a radius of 2.0 cm. If the bulk modulus of copper is 130 GPa, calculate
To calculate the change in volume of the copper sphere due to the applied pressure, we can use the formula:
ΔV = V * (∆P / B)
where:
- ΔV is the change in volume,
- V is the initial volume of the sphere,
- ∆P is the change in pressure, and
- B is the bulk modulus of copper.
First, we need to calculate the initial volume of the copper sphere using the formula for the volume of a sphere:
V = (4/3) * π * r^3
Given that the radius of the sphere is 2.0 cm, we can substitute this value into the formula:
V = (4/3) * π * (2.0 cm)^3
Now that we have the initial volume, we can calculate the change in volume using the values given:
ΔP = 200 MPa = 200 x 10^6 Pa
B = 130 GPa = 130 x 10^9 Pa
Substituting these values into the formula for ΔV, we obtain:
ΔV = V * (∆P / B)
= [(4/3) * π * (2.0 cm)^3] * [(200 x 10^6 Pa) / (130 x 10^9 Pa)]
Evaluate this expression to obtain the change in volume.
Finally, to calculate the change in volume numerically, substitute the values and perform the calculations.