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 = 17.3 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" (see figure), and is typically H = 1.5 cm for a 750-mL bottle filled at 20

Wine bottles are never completely filled: a small volume of air is left in the glass bottle's cylindrically shaped neck (inner diameter d = 17.3 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" (see figure), and is typically H = 1.5 cm for a 750-mL bottle filled at 20 degree 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 Hif the bottle is kept at the following temperatures. 11 degree C cm 32 degree C cm

Explanation / Answer

coefficient of alchohol = 2*0.000214 = 0.000428

dV = r*V*dT = 0.000428*750*-9 = -2.889 ml = -2.889*10^-6 m^3

-dV = H*pi*d^2/4

h = 1.22 cm

H = 1.5+1.22 = 2.72 cm

b) dV = r*V*dT = 0.000428*750*12 = 3.852 ml = 3.852*10^-6 m^3

dV = H*pi*d^2/4
H = 1.63 cm

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