Question

An automobile tire has a volume of 1.62 x 10^-2 m³ and contains air at a gauge pressure (pressure above atmospheric pressure) of 164 kPa when the temperature is 0.00°C. What is the gauge pressure of the air in the tires when its temperature rises to 21.8°C and its volume increases to 1.68 x 10^-2 m³? Assume atmospheric pressure is 1.01 x 10⁵ Pa.

Answer 1

Atmospheric pressure = P_atm = 1.01 x 10⁵ Pa

Initial gauge pressure of the air in the tire = P_1g = 164 kPa = 164 x 10³ Pa = 1.64 x 10⁵ Pa

Initial absolute pressure of the air in the tire = P₁

P₁ = P_1g + P_atm

P₁ = 1.64x10⁵ + 1.01x10⁵

P₁ = 2.65 x 10⁵ Pa

Initial volume of the tire = V₁ = 1.62 x 10^-2 m³

Initial temperature of the air in the tire = T₁ = 0 ^oC = 0 + 273 K = 273 K

Final absolute pressure of the air in the tire = P₂

Final volume of the tire = V₂ = 1.68 x 10^-2 m³

Final temperature of the air in the tire = T₂ = 21.8 ^oC = 21.8 + 273 K = 294.8 K

P₂ = 2.76 x 10⁵ Pa

Final gauge pressure of the air in the tires = P_2g

P_2g = P₂ - P_atm

P_2g = 2.76x10⁵ - 1.01x10⁵

P_2g = 1.75 x 10⁵ Pa

Final gauge pressure of the air in the tires = 1.75 x 10⁵ Pa