Question

An automobile tire at 30°C has a pressure of 3.00 atm. Temperature decreases to -5°C. Assume that there is no volume change in the tire. How does the tire pressure change in response to the temperature change?

Answer 1

The tire pressure drops to 2.65 atm.

Step-by-step explanation:

Volume remains constant, so we can use Gay-Lussac’s Law.

p₁/T₁ = p₂/T₂ Multiply both sides by T₂

p₂ = p₁ × T₂/T₁

Data:

p₁ = 3.00 atm; T₁ = 30.0 °C

p₂ = ?; T₂ = -5 °C

Calculations:

(a) Convert the temperatures to kelvins

T₁ = 30.0 + 273.15 = 303.15 K

T₂ = -5 + 273.15 = 268.15 K

(b) Calculate the new pressure

p₂ = 3.00 × 268.15/303.15

p₂ = 3.00 × 0.8845

p₂ = 2.65 atm

The pressure drops to 2.65 atm.