A moonshiner makes the error of filling a glass jar to the brim and capping it tightly. The moonshine expands more than the glass when it warms up, in such a way that the volume increases by 0.4% (that is, ΔV/V0 = 4 ✕ 10-3) relative to the space available. Calculate the force exerted by the moonshine per square centimeter if the bulk modulus is 1.6 ✕ 109 N/m2, assuming the jar does not break..

ΔP = (640 N/cm^2)

Explanation:

Given:-

- The volume increase, ΔV/V0 = 4 ✕ 10^-3

- The Bulk Modulus, B = 1.6*10^9 N/m^2

Find:-

Calculate the force exerted by the moonshine per square centimeter

Solution:-

- The bulk modulus B of a material is dependent on change in pressure or Force per unit area and change in volume by the following relationship.

                                  B = ΔP / [(ΔV/V)]

- Now rearrange the above relation and solve for ΔP or force per unit area.

                                  ΔP = B* [(ΔV/V)]

- Plug in the values:

                                  ΔP = (1.6*10^9)*(4 ✕ 10^-3)

                                  ΔP = 6400000 N/m^2

- For unit conversion from N/m^2 to N/cm^2 we have:

                                  ΔP = (6400000 N/m^2) cm^2 / (100)^2 m^2

                                  ΔP = (640 N/cm^2)

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