Question

An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 26.0% of its original volume and the temperature is increased to 46.0°C. (a) What is the tire pressure in pascals? Pa (b) After the car is driven at high speed, the tire's air temperature rises to 85.0°C and the tire's interior volume increases by 3.00%. What is the new tire pressure (absolute) in pascals? Pa

Answer 1

Initial pressure of the air = P₁ = 1.013 x 10⁵ Pa (Atmospheric pressure)

Initial volume of the air = V₁

Initial temperature of the air = T₁ = 10 ^oC = 10 + 273 K = 283 K

Pressure of the air in the tire = P₂

Volume of the air in the tire = V₂

The air is compressed to 26% of its original volume when the tire is filled with air.

V₂ = 0.26V₁

Temperature of the air in the tire = T₂ = 46 ^oC = 46 + 273 K = 319 K

P₂ = 4.392 x 10⁵ Pa

New pressure of the air in the tires after the car is driven at high speed = P₃

Volume of the air after the car is driven at high speed = V₃

The tire's interior volume increases by 3% after the car is driven at high speed.

V₃ = 1.03V₂

Temperature of the air in the tire after the car is driven at high speed = T₃ = 85 ^oC = 85 + 273 K = 358 K

P₃ = 4.785 x 10⁵ Pa

a) Pressure of the air in the tires = 4.392 x 10⁵ Pa

b) Pressure of the air in the tires after the car is driven at high speed = 4.785 x 10⁵ Pa