Question

The gauge pressure in your car tires is 2.55 × 105 Pa at a temperature of 35.0°C when you drive it onto a ferry boat to Alaska. What is the gauge pressure of the tires, in pascals, later when the temperature has dropped to -40.0°C? Assume the volume of each tire does not change.

Answer 1

Atmospheric pressure = P_atm = 1.013 x 10⁵ Pa

Initial gauge pressure in the car tire = P_1g = 2.55 x 10⁵ Pa

Initial temperature = T₁ = 35 ^oC = 308 K

Initial absolute pressure in the car tire = P₁

P₁ = P_1g + P_atm

P₁ = 2.55x10⁵ + 1.013x10⁵

P₁ = 3.563 x 10⁵ Pa

Final absolute pressure in the car tire = P₂

Final temperature = T₂ = -40 ^oC = 233 K

Volume of the tires does not change.

P₂ = 2.695 x 10⁵ Pa

Final gauge pressure in the car tire = P_2g

P₂ = P_2g + P_atm

2.695x10⁵ = P_2g + 1.013x10⁵

P_2g = 1.682 x 10⁵ Pa

Gauge pressure in the tires when the temperature has dropped to -40 ^oC = 1.682 x 10⁵ Pa