# Why is my tire flat?

This has been a very cold winter (written in February 2014). One cold morning I noticed that my car tires seemed very “flat”. Here is a cold weather gas law question for your students.

My car tire pressures were adjusted by the auto shop technician using a tire pressure gauge1 with the air at a temperature of 20°C. The gauge setting was 30.00 psi (lb/in2) or 206.8 kPa.2 Ambient pressure was one atmosphere, or 14.70 psi or 101.33 kPa. After a cold night, the air in the tires was at –25°C, and the tires seemed “flat”.

As an approximation, assume that the air in the tires is at constant volume, that the air behaves as an ideal gas1 and that ambient pressure remains one atmosphere.

1. What is the ratio of the new cold air pressure to the former warm air pressure in the tires?
2. What is the new gauge pressure in the tires?

(b) 23.14 psi or 159.5 kPa (not 25.40 psi)

## References

1. Wikipedia for: gauge pressures; gas laws; kelvin temperature.
2. Professor Wildi’s Visualization of Units Page for Pressure: http://www.wildi-theo.com/fichiers/documents/contenu/charts/pressure_and_stress.pdf.