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 24.0% of its original volume and the temperature is increased to 48.0°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 = 101325 Pa

Initial volume of the air = V₁

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

Pressure of the air after it is compressed into the tires = P₂

Volume of the air after it is compressed into the tires = V₂

The air is compressed to 24% of it's original volume.

V₂ = 0.24V₁

Temperature of the air after it is compressed into the tires = T₂ = 48 ^oC = 48 + 273 K = 321 K

P₂ = 4.79 x 10⁵ Pa

Pressure of the air in the tires after the car is driven = P₃

Volume of the air in the tires after the car is driven = V₃

The tire's interior volume increases by 3%.

V₃ = 1.03V₂

Temperature of the air in the tires after the car is driven = T₃ = 85 ^oC = 85 + 273 K = 358 K

P₃ = 5.19 x 10⁵ Pa

a) Pressure in the tires = 4.79 x 10⁵ Pa

b) Pressure in the tires after the car is driven at high speed = 5.19 x 10⁵ Pa