Walking along the beach on your summer vacation, you come across a corked bottle
ID: 1475243 • Letter: W
Question
Walking along the beach on your summer vacation, you come across a corked bottle containing a message. You assume the air in the bottle is at atmospheric pressure and the temperature is 30 degree C. In order to get the cork out of the bottle, you decide to hold the bottle in a fire, figuring the increased pressure will eventually push out the cork. At about 95 degree C, the cork is ejected from the bottle. What is the pressure in the bottle just before the cork is pushed out? Please show all work and calculations.Explanation / Answer
from ideal gas equation
PV =nRT
Here volume and number of moles in the bottle are constant so
P is directly proportional to the temperature
P1/P2 = T1/T2
P2 = P1T2/T1
given P1 = 1 atm = 1.01*10^5 Pa, T1 = 300C = 303 k, T2 = 950C = 368 k
P2 = 1.01*10^5*368 / 303
= 122666.67 Pa
P2 = 1.2266667 atm
Pressure inside the bottle at 95 0c is 1.22 atm
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