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 12.6°C is opened, then closed, and then left in a closed car with an internal temperature of 76.0°C. Neglecting the thermal expansion of the water and the bottle, find the pressure (in atm) 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

at temparature T1 = 12.6 c the pressure is the atmospheric pressure = 1 atm

at temparature T2 = 76 C,the pressure is P2 = ?

using ideal gas equation at constant volume

P1/P2 = T1/T2 = (273+12.6)/(273+76) = 0.818

P2 = P1/0.818 = 1 atm/0.818 = 1.22 atm

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