The pressure in an automobile tire is 204 kPa at 29 C. At the end of a trip on a hot sunny day, the pressure has risen to 300 kPa. What is the temperature of the air in the tire?

Answer 1

Given:

P1 = initial pressure = 204 kPa

T1 = initial temperature = 29ºC + 273 = 302K (note: when dealing with gases, use Kelvin)

P2 = final pressure = 300 kPa

Asked for:

T2: final temperature = ?

If we assume that the volume of the tire is constant, then we are dealing with Gay-Lussac's Law:

P1/T1 = P2/T2 and solving for T2 we have...

T2 = P2T1/P1

T2 = (300 kPa)(302K)/204 kPa

T2 = 444 degrees Kelvin

If you want this in degrees Celsius, simply subtract 273 to obtain 171 degrees Celsius.