Problem 41PE

A farmer making grape juice fills a glass bottle to the brim and caps it tightly. The juice expands more than the glass when it warms up, in such a way that the volume increases by 0.2% (that is, ΔV / V0 = 2×10−3) relative to the space available. Calculate the magnitude of the normal force exerted by the juice per square centimeter if its bulk modulus is 1.8×109 N/m2 , assuming the bottle does not break. In view of your answer, do you think the bottle will survive?

Solution 41PE

Step 1 of 4

The juice inside the glass expands with the increased volume of 0.2 %, when it warms up . Here we need to calculate the magnitude of the normal force exerted by juice per unit square centimeter if the bulk modulus is . Also, we need to comment whether the glass will survive this pressure.

Given data,

The ratio of change in volume to original volume,

Bulk modulus,

To find,

Force per unit area,