Question

A car tire is fully inflated to a pressure of 32 psi at 25 °C. After driving for 2 hours, the volume of the tire is unchanged, but pressure of the tire is now 36 psi. What is the new temperature of the gas inside the tire?

What caused this change?

Answer 1

50.5°C

Step-by-step explanation:

Start with the ideal gas law:

PV = nRT

Rearranging:

P/T = nR/V

Since the right side is constant (volume and mass don't change):

P₁ / T₁ = P₂ / T₂

This equation is also known as Gay-Lussac's law. Plugging in the values (make sure to use absolute pressure and temperature):

(32 psi + 14.7 psi) / (25 + 273.15) K = (36 psi + 14.7 psi) / T

Solving for T:

T = 323.69 K

T = 50.5°C