A liquid compressed in a cylinder has a volume of 1000 cm^3 at 1 MN/m^2 and a volume of 995 cm^3 at 2 MN/m^2. What is its bulk modulus of elasticity?QUESTION 7ANSWERa.0.67 MPab.0.2 MPac.670 MPad.200 MPa
Question
A liquid compressed in a cylinder has a volume of 1000 cm^3 at 1 MN/m^2 and a volume of 995 cm^3 at 2 MN/m^2. What is its bulk modulus of elasticity?QUESTION 7ANSWERa.0.67 MPab.0.2 MPac.670 MPad.200 MPa
Solution
The bulk modulus of elasticity (K) is a measure of a substance's resistance to uniform compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.
The formula for bulk modulus (K) is:
K = -V * (ΔP/ΔV)
where: V is the initial volume, ΔP is the change in pressure, and ΔV is the change in volume.
Given in the problem: V = 1000 cm^3 = 1 x 10^-3 m^3 (since 1 m^3 = 1 x 10^6 cm^3) ΔP = 2 MN/m^2 - 1 MN/m^2 = 1 MN/m^2 = 1 x 10^6 N/m^2 (since 1 MN/m^2 = 1 x 10^6 N/m^2) ΔV = 995 cm^3 - 1000 cm^3 = -5 cm^3 = -5 x 10^-6 m^3
Substituting these values into the formula, we get:
K = -(1 x 10^-3 m^3) * ((1 x 10^6 N/m^2) / (-5 x 10^-6 m^3)) K = 200 GPa
However, the options are given in MPa, so we need to convert GPa to MPa. Since 1 GPa = 1000 MPa, we get:
K = 200,000 MPa
None of the options match this result. There might be a mistake in the problem or the options provided.
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