Water bottle in a hot car. In the American Southwest, the temperature in a close

Question

Water bottle in a hot car. In the American Southwest, the temperature in a closed car parked in sunlight during the summer can be high enough to burn flesh. Suppose a bottle of water at a refrigerator temperature of 4.23°C is opened, then closed, and then left in a closed car with an internal temperature of 75.8°C. Neglecting the thermal expansion of the water and the bottle, find the pressure in the air pocket trapped in the bottle. (The pressure can be enough to push the bottle cap past the threads that are intended to keep the bottle closed.)

Explanation / Answer

water at a refrigerator temperature of 4.23°C

internal temperature of 75.8°C

initial temparature of the water is

Ti=4.23 0C

=277.38 K

internal temparature i.e final temparature is

Tf=75.8 0C

=348.95 K

initial pressure Pi= 1atm

from the ideal gas equation PV=nRT

here n is the number of moles is constant and R is universal gas constant is also constant

in this problem volume also constant

Pi/Pf=Ti/Tf

Pf = Pi (Tf/Ti )

=348.95 /277.38

= 1.258 atm

pressure in the air pocket trapped in the bottle.is 1.258 atm

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