Question
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, $\dfrac{\Delta V}{V_o} = 2 \times 10^{-3}$) relative to the space available. Calculate the magnitude of the normal force exerted by the juice per square centimeter if its bulk modulus is $1.8 \times 10^9 \textrm{ N/m}^2$, assuming the bottle does not break. In view of your answer, do you think the bottle will survive?

$360 \textrm{ N/cm}^2$. This is like $36 \textrm{ kg}$ supported by $1 \textrm{ cm}^2$ of glass. It will probably break.

Solution Video