5.3 Exercise 21

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, $Δ V / V_{0} = 2 \times \text{10}^{- 3}$) relative to the space available. Calculate the magnitude of the normal force exerted by the juice per square centimeter if its bulk modulus is $1 . 8 \times \text{10}^{9} \text{N}/\text{m}^{2}$, assuming the bottle does not break. In view of your answer, do you think the bottle will survive?