Determine the bulk modulus of elasticity of a liquid, if the pressure is increased from 7N/m^2 to 13N/m^2. The volume of the liquid decrease by 0.15%
To determine the bulk modulus of elasticity of a liquid, you need to use the formula:
Bulk modulus (K) = -V * ΔP / ΔV
where:
- K is the bulk modulus of elasticity,
- V is the volume of the liquid,
- ΔP is the change in pressure, and
- ΔV is the change in volume.
In this case, the pressure is increased from 7N/m^2 to 13N/m^2, and the volume of the liquid decreases by 0.15%. To find the bulk modulus, we need to calculate ΔP and ΔV.
ΔP = Final pressure - Initial pressure
= 13N/m^2 - 7N/m^2
= 6N/m^2
ΔV = (Change in volume percentage / 100) * Initial volume
= (0.15 / 100) * Initial volume
Since we know the change in volume percentage but not the initial volume, we can't find ΔV directly. However, we can rewrite the equation as follows:
ΔV = (Change in volume percentage / 100) * Final volume
We can then find the bulk modulus using the updated ΔV formula:
K = -V * ΔP / ΔV
= -V * ΔP / ((Change in volume percentage / 100) * Final volume)
Given that the volume decreases, we use a negative sign.
To calculate the bulk modulus, you would need to know the final volume of the liquid. If you have that information, you can substitute the values into the equation and solve for K.