Question

The gauge pressure in your car tires is 2.50×10⁵ N/m² at a temperature of 35.0°C when you drive it onto a ship in Los Angeles to be sent to Alaska. What is their gauge pressure on a night in Alaska when their temperature has dropped to −40.0°C ? Assume the tires have not gained or lost any air.

a) 1.68 × 10⁵ N/m²

b) 2.50 × 10⁵ N/m²

c) 3.85 × 10⁵ N/m²

d) 4.92 × 10⁵ N/m²

Answer 1

Using Gay-Lussac's Law and converting temperatures to Kelvin, the gauge pressure in the tires when the temperature drops to -40.0°C is calculated to be approximately 1.89 × 10^5 N/m². This result is not reflected in the answer choices provided, indicating a potential error in the question's options or the calculation.

Step-by-step explanation:

To solve for the gauge pressure in the tires at a lower temperature, we can use the combined gas law, which relates pressure, volume, and temperature of a gas. However, since the volume of the tires does not change, we can use a simplified version of the law that relates only pressure and temperature, commonly referred to as Gay-Lussac's Law:

P1/T1 = P2/T2

Where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature. Remember to convert temperatures to Kelvin:

T1 = 35.0°C + 273.15 = 308.15 K
T2 = -40.0°C + 273.15 = 233.15 K

We are given P1 as 2.50 × 10^5 N/m² and need to solve for P2, so we rearrange the equation to solve for P2:

P2 = P1 × (T2/T1)

P2 = 2.50 × 10^5 N/m² × (233.15 K / 308.15 K)

Calculating P2, we find that the gauge pressure in Alaska would be:

P2 = 2.50 × 10^5 N/m² × (0.7565)

P2 ≈ 1.89 × 10^5 N/m²

This is not one of the answer choices provided, suggesting a possible mistake in the options given or in the calculation. This can happen if temperatures are not correctly converted to Kelvin or if a rounding error occurs. It's important to double-check calculations and ensure that the proper formulae and conversions are used.