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", 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.

1.Estimate H if the bottle is kept at 32 C.

Explanation / Answer

Increase in volume of wine = Vo (alpha) (delta T)
Vo is initial volume of wine = 750 mL
alpha is coefficient of volumetric expansion of wine = 2 time that of water = 4.28x10-4 per C
Delat T is change in tempreture = 32- 20 = 12 C
change in volume = 750*4.28x10-4 * 12 = 3.852 mL =3.852 cm3
Decrease in headspace due to increase in volume = increase in volume / Area
= 3.852 / (pi d2/4) = 3.852*4 / 3.14*1.852 = 1.43 cm
H at 32 C = 1.5 - 1.43 = 0.07 cm

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