Final answer:
The gauge pressure of a car tire will decrease with a drop in temperature as per Gay-Lussac's law. Using the formula P2 = P1 (T2/T1), the new gauge pressure after a temperature change from 35.0°C to -40.0°C can be calculated. Actions such as inflating the tire may be necessary if the pressure is below the recommended operational range.
Step-by-step explanation:
When we consider the effects of temperature changes on the gauge pressure of a car tire, it's essential to apply the principles of gas laws, specifically the Gay-Lussac's law. This law states that the pressure of a gas of fixed mass and fixed volume is directly proportional to the gas's absolute temperature (measured in Kelvin). Accordingly, if the tire pressure is 214-218 psi at a higher temperature, a decrease in temperature will result in a decrease in pressure.
To determine the new gauge pressure after the temperature change, the following formula, which is derived from Gay-Lussac's law, can be used: P2 = P1 (T2/T1), where P1 is the initial pressure, T1 is the initial temperature, T2 is the final temperature, and P2 is the final pressure.
If the initial gauge pressure of the main landing gear tire is 214-218 psi at a temperature of 35.0°C (308.15 K), and the temperature drops to -40.0°C (233.15 K), the final pressure can be calculated by the proportion P2 = 214-218 psi * (233.15 K / 308.15 K). This calculation must be done for the specific initial pressure within the range given to find the corresponding final pressure.
If the final pressure calculated is below the manufacturer's recommended pressure range for safe operation, the tire would need to be inflated to restore it to the correct pressure. If the pressure is still within safe operational limits, then further action may not be required. However, it is always essential to consult the aircraft or vehicle's maintenance manual for the precise procedures and the recommended pressure ranges for safety.