An automobile tire is filled to an absolute pressure of 30 a

An automobile tire is filled to an absolute pressure of 3.0 atm at a temperature of 30 degree C. Later it is driven to a place where the temperature is only -20 degree C. What is the absolute pressure of the tire at the cold place?

Solution

Initial pressure P = 3 atm

Initial temprature T = 30 ^o C

                            =30 + 273

                            = 303 K

Final temprature T \' = -20 ^oC

                             = -20 +273

                             =253 K

Final pressure P \' = ?

At constant volume , P \' / P = T \' / T        Since pressure is directly proportional to absolute temprature.

P \' = ( T \' /T ) P

      = (253/303) 3atm

      = 2.504 atm