Question

On a spring morning (20C) you fill your tires to a pressure of 2.25 atmospheres. As you ride along, the tire heats up to 45C from the friction on the road. What is the pressure in your tires now?

Answer 1

To find the new tire pressure at 45°C, use the combined gas law and convert temperatures to Kelvin. Solve the formula P1/T1 = P2/T2, revealing that the final pressure will be approximately 2.44 atmospheres.

Step-by-step explanation:

Calculating Pressure Changes Due to Temperature Changes: Tire Pressure

The pressure in tires is directly proportional to temperature when volume and the amount of gas remain constant. This relationship is described by the combined gas law, which is a combination of Boyle's, Charles's, and Gay-Lussac's laws. When you fill your tires at 20°C with a pressure of 2.25 atmospheres, and the temperature rises to 45°C, we need to calculate the new pressure.

First, convert temperatures to Kelvin by adding 273.15:

• Initial temperature: 20°C + 273.15 = 293.15 K
• Final temperature: 45°C + 273.15 = 318.15 K

We use the formula P1/T1 = P2/T2, where P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure, and T2 is the final temperature.

Then:

2.25 atm / 293.15 K = P2 / 318.15 K

Multiplying both sides of the equation by the final temperature (318.15 K) and solving for P2 gives:

P2 = (2.25 atm) * (318.15 K) / (293.15 K)

Final Pressure P2 = 2.44 atm

The pressure in the tires after heating up would be approximately 2.44 atmospheres.

Answer 2

Assuming the volume of the tire remains constant, we can use the ideal gas law to determine the pressure of the tire at the higher temperature:

P1/T1 = P2/T2

where P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure (what we're trying to find), and T2 is the final temperature.

Converting the temperatures to Kelvin (as the ideal gas law requires temperatures in Kelvin), we have:

P1/T1 = P2/T2

P1 = 2.25 atm

T1 = 20 + 273.15 = 293.15 K

T2 = 45 + 273.15 = 318.15 K

Solving for P2, we get:

P2 = P1(T2/T1)

P2 = 2.25 atm (318.15 K / 293.15 K)

P2 = 2.44 atm (rounded to two significant figures)

Therefore, the pressure in your tires at 45°C would be approximately 2.44 atm.