Final answer:
To calculate the new gauge pressure after a temperature drop, the Ideal Gas Law is used. The initial pressure is adjusted for the change in temperature, yielding a new gauge pressure of approximately 1.90 × 10⁵ N/m².
Step-by-step explanation:
The gauge pressure in a car tire at an initial temperature can be compared to the gauge pressure at a different temperature using the Gas Laws. To find the new gauge pressure after a temperature change, we can use the Ideal Gas Law in the form of the combined gas law for constant volume, which is P1/T1 = P2/T2, where P is the pressure and T is the temperature in Kelvins.
Given the initial gauge pressure P1 = 2.50 × 105 N/m² at an initial temperature of T1 = 35.0°C, we convert this to Kelvin by adding 273.15 to get T1 = 308.15 K. The final temperature T2 is given as -40.0°C, or 233.15 K in Kelvins.
Applying the formula:
P2 = P1 × (T2/T1)
P2 = (2.50 × 105 N/m²) × (233.15 K / 308.15 K)
P2 = 1.90 × 105 N/m² (approximately)
Therefore, the gauge pressure at -40.0°C will be roughly 1.90 × 105 N/m².