Wine bottles are never completely filled: a small volume of air is left in the g

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"(Figure 1) , 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 at 30 ?C.

Explanation / Answer

As T increases, so the headspace decreases,
T = +10degC

H = -p*V0*T / pi*r^2

= ((420 *10^-6) * (0.750) ) / (pi*(0.00925)^2)

= 1.171 cm

= 0.0117 m

So, H = 1.5 - 1.17 cm

= 0.33 cm

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