Question

The air pressure in the tires of an automobile is adjusted to 26.0 psi at a gas station in San Diego, where the air temperature is 68°F. The air in the tires is at the same temperature as the atmosphere. The automobile is then driven east along a hot desert highway, and the temperature inside the tires reaches 145 °F. What is the pressure in the tires? _______ psi

Answer 1

Given,

Pressure in the tire in San Diego(P₁) = 26.0 psi

The temperature in the tire at San Diego(T₁) = 68 ^oF

The temperature inside the tire along a hot desert highway(T₂) = 145 ^oF

Converting the pressure, from psi to atm,

We know, 1 atm = 14.6959 psi

= 26.0 psi x ( 1 atm / 14.6959 psi)

P₁ = 1.7692 atm

Now, Converting the temperature from ^oF to K,

T₁ = (68 -32) /1.8 = 20 ^oC + 273.15 = 293.15 K

T₂ = ( 145 - 32) /1.8 = 62.78 ^oC + 273.15 = 335.93 K

Now, We know the Gay-Lussac's law formula for P and T,

P₁ /T₁ = P₂ /T₂

Rearranging the formula,

P₂ = (P₁T₂) / T₁

P₂ = (1.7692 atm x 335.93 K) / 293.15 K

P₂ = 2.027 atm

Converting atm to psi,

= 2.027 atm x (14.6959 psi/ 1 atm)

= 29.8 psi Or 30. psi