Question

Wine bottles are never completely filled: a small volume of air is left in the glass bottle’s cylindrically shaped neck (inner diameter d=18.5 mm) to allow for wine’s fairly large coefficient of thermal expansion. the distance h between the surface of the liquid contents and the bottom of the cork is called the "headspace height" and is typically h=1.5 cm for a 750-ml bottle filled at 20°c. due to its alcoholic content, wine’s coefficient of volume expansion is about double that of water; in comparison, the thermal expansion of glass can be neglected. estimate h if the bottle is kept (a) at 10°c, (b) at 30°c.

Answer 1

The headspace in a wine bottle allows for the expansion of wine with temperature changes to avoid breakage. The headspace height will increase or decrease with rising or falling temperatures, respectively. Exact values for changes in headspace height require the specific coefficient of volume expansion for wine.

Step-by-step explanation:

When calculating the expansion of wine in a bottle due to temperature changes, we must consider the thermal expansion of liquids, which is significantly greater than the expansion of glass. As the temperature increases, the wine will expand more than the glass, potentially leading to a breakage if there's no air in the headspace.

This headspace provides a cushion for the expansion of the liquid and prevents the bottle from breaking. Therefore, wine bottles are never completely filled.

To estimate the height h for different temperatures, we need to consider the coefficient of volume expansion which is roughly double that of water due to the alcoholic content.

To calculate the change in height h due to a change in temperature, we can use the initial headspace height, bottle volume, and coefficient of volume expansion.

However, without the specific coefficient of volume expansion for wine, we can only say that the headspace height will decrease as the temperature drops (since the wine contracts) and increase as the temperature rises (since the wine expands). The exact values require additional information.