Compute the volume change of solid copper cube, 40mm on edge, when subjected to a pressure of 20MPa. The bulk modulus for copper is 125GPa
I want the answer
To compute the volume change of a solid copper cube under a certain pressure, you need to use the equation for bulk modulus. The bulk modulus (K) relates the pressure (P) applied to a material to the resulting relative volume change (dV/V) experienced by the material. The equation is:
K = -V * (dP/dV)
Where:
- K is the bulk modulus
- V is the initial volume of the material
- dP is the change in pressure applied to the material
- dV is the resulting volume change
- dV/V is the relative volume change
In this case, we want to find the volume change (dV) of a solid copper cube with an edge length of 40mm when subjected to a pressure of 20MPa. The bulk modulus for copper is given as 125GPa (which is equivalent to 125 * 10^9 Pa).
Let's solve it step by step:
Step 1: Convert the edge length from millimeters to meters.
40mm = 40/1000 = 0.04 meters (since there are 1000 millimeters in a meter)
Step 2: Calculate the initial volume of the copper cube.
The initial volume (V) of a cube is given by V = (edge length)^3.
So, V = (0.04)^3 = 0.000064 cubic meters
Step 3: Convert the pressure from megapascals to pascals.
20MPa = 20 * 10^6 Pa (since there are 1 million pascals in a megapascal)
Step 4: Substitute the values into the bulk modulus equation.
K = -V * (dP/dV)
125 * 10^9 = -0.000064 * (dP/0.000064)
Step 5: Rearrange the equation to solve for dP (change in pressure).
dP = K * (dV/V)
dP = 125 * 10^9 * (dV/0.000064)
Step 6: Substitute the given bulk modulus value and calculate dP.
dP = 125 * 10^9 * (dV/0.000064)
dP = 1.953 * 10^9 * (dV)
At this point, we need to know the actual value of dV (the relative volume change) to calculate the volume change of the copper cube. Unfortunately, the problem statement doesn't provide this information. You would need to know how the volume changes with the given pressure or have additional data to calculate the volume change accurately.
Please provide the information needed to calculate the relative volume change (dV), and then we can proceed to determine the volume change of the copper cube.