Question
Ch17-sec 4 Wine bottles are never completeley filled: a small volume ofair is left in the glass bottle's cylindrically shaped neck (innerdiameter d= 18.5mm) to allow for wine's fairly large coefficient ofthermal expansion. the distance H between the surface of the liquidcontents and the bottom of the cork is called the headspace height"(fig 17-21 on the book), and is typically H = 1.5 cm for a 750-mLbottle filled a 20 Celsius. Due to its alcoholic content, wine'scoefficient of volume expansion is about that of water; incomparison, the thermal expansion of glass can be neglected.Estimate H if the bottle is kept (a) at 10 Celsius (b) at 30Celsius. Ch17-sec 4 Wine bottles are never completeley filled: a small volume ofair is left in the glass bottle's cylindrically shaped neck (innerdiameter d= 18.5mm) to allow for wine's fairly large coefficient ofthermal expansion. the distance H between the surface of the liquidcontents and the bottom of the cork is called the headspace height"(fig 17-21 on the book), and is typically H = 1.5 cm for a 750-mLbottle filled a 20 Celsius. Due to its alcoholic content, wine'scoefficient of volume expansion is about that of water; incomparison, the thermal expansion of glass can be neglected.Estimate H if the bottle is kept (a) at 10 Celsius (b) at 30Celsius.
Explanation / Answer
The linear expansion is lt = lo* (1 + t) or lo= (lt/(1 + t))-----------(1) lt= 1.5 cm = 1.5 * 10-2 m = 69 * 10-6/K t = (20 - 0) oC = 20 oC = (20 +273) K = 293 K substituting the above values in equation (1) we get the valueof lo(the distance H between the surface of the liquidcontents and the bottom of the cork) (a)the value of H when t = 10 oC is H10= Ho* (1 + t) Ho= lo and t = (10 - 20)oC = -10 oC = (-10 + 273) K = 263 K (b)the value of H when t = 30 oC is H30= Ho* (1 + t) t = (30 - 20) oC = 10 oC = (10 +273) K = 283 K