Question

Most cars need tires filled to 32.0 - 35.0 psi. Your tires are filled to 32.1 psi at the beginning of the month where the temperature is on average 12.5 degree C. At the end of the mounth the average temperture has dropped to -3.1 C. Are the tires still safe to drive on?

Answer 1

Answer: No it is not safe to drive on.

Explanation:

To calculate the final pressure of the system, we use the equation given by Gay-Lussac Law. This law states that pressure of the gas is directly proportional to the temperature of the gas at constant pressure.

Mathematically,

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

where,

$P_1\text{ and }T_1$ are the initial pressure and temperature of the gas.

$P_2\text{ and }T_2$ are the final pressure and temperature of the gas.

We are given:

$P_1=32.1psi\\T_1=12.5^0C=(273+12.5)K=285.5K\\P_2=?psi=27.5psi\\T_2=-3.1^0C=(273-3.1)K=269.9K$

Putting values in above equation, we get:

$\frac{32.1}{285.5K}=\frac{P_2}{269.9}\\\\P_2=30.3psi$

As the pressure lies below the recommended range of 32.0-35.0 psi. Thus it is not safe to drive on