A fractional change in the volume of oil is 1percent when a pressure of 2×10^7N/m^2 is applied.calculatebthe bulk modulus and it's compression factor
To calculate the bulk modulus and compression factor, we need to use the formula that relates pressure, volume, and the bulk modulus.
The formula is:
ΔV/V = -B ΔP
Where:
- ΔV/V represents the fractional change in volume.
- B represents the bulk modulus.
- ΔP represents the change in pressure.
Given that the fractional change in volume (ΔV/V) is 1%, which is equivalent to 0.01, and the pressure change (ΔP) is 2×10^7 N/m^2, we can rearrange the formula to solve for the bulk modulus (B).
First, let's calculate the bulk modulus:
0.01 = -B × 2×10^7 N/m^2
Dividing both sides of the equation by 2×10^7 N/m^2:
0.01 / 2×10^7 N/m^2 = -B
Therefore, the bulk modulus is:
B = -0.01 / 2×10^7 N/m^2
Now, to calculate the compression factor, we need to use the following formula (assuming an isothermal process):
Compression factor (Z) = V / V0
Where:
- V represents the final volume.
- V0 represents the initial volume.
Since ΔV = V - V0, we can rewrite the formula as:
Z = (V0 + ΔV) / V0
Given that ΔV/V = -0.01 and Z = V / V0, we substitute and rearrange the formula:
Z = (V0 - 0.01 × V0) / V0
Simplifying the equation:
Z = (1 - 0.01) = 0.99
Therefore, the compression factor is 0.99.