Question

A bicycle tires is inflated to a pressure of 4110 torr at 29.0°c. if the maximum pressure the tire can withstand before bursting is 7110 torr, at what temperature, in °c, will th burst? assume that the volume of the tire does not change as it is heated.

Answer 1

To find the temperature at which a bicycle tire will burst, apply Gay-Lussac's law, P1/T1 = P2/T2, adjust for Kelvin, and solve for T2.

Step-by-step explanation:

The question is about calculating the temperature at which a bicycle tire will burst due to increased pressure when it's already inflated to a certain level at a known temperature. By using the ideal gas law, we can predict the tire bursting temperature assuming the volume of the tire remains constant and there are no leaks.

To calculate this, we will apply the Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its absolute temperature when the volume is constant (P/T = k). Here, P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure (maximum pressure before bursting), and T2 is the final temperature (temperature at which the tire will burst).

To find T2, we rearrange the law to T2 = (P2/P1) * T1. Using the initial conditions provided (P1 = 4110 torr, T1 = 29.0°C + 273.15 to convert to Kelvin), and the bursting pressure (P2 = 7110 torr), we calculate T2 in Kelvin, then convert back to °C by subtracting 273.15. Plugging in the numbers, we would calculate T2, and that will be the temperature at which the tire will burst.