(b) If a car tire is filled to a pressure of 220.6 kPa measured at 24 °C, what will be the tire pressure if the tires heat up to 49 °C during driving?

Verified step by step guidance

1. Step 1: Recognize that this problem is asking you to apply the ideal gas law in the form of Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its absolute temperature, assuming volume and the amount of gas are constant. The formula is P1/T1 = P2/T2, where P is pressure and T is temperature.
2. Step 2: Convert the temperatures from Celsius to Kelvin by adding 273.15 to each. This is because the ideal gas law and its related laws use absolute temperature scales, which in SI units is the Kelvin scale.
3. Step 3: Substitute the given values into the formula. P1 is the initial pressure (220.6 kPa), T1 is the initial temperature (24 °C in Kelvin), and T2 is the final temperature (49 °C in Kelvin). We are solving for P2, the final pressure.
4. Step 4: Rearrange the formula to solve for P2. This gives P2 = P1 * (T2/T1).
5. Step 5: Plug in the values from step 3 into the formula from step 4 and solve for P2. This will give you the final pressure of the tire after it has heated up.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this context, it helps us understand how the pressure of the gas in the tire changes with temperature, assuming the volume remains constant.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. Although the volume of the tire does not change, this law illustrates how temperature affects pressure, which is crucial for calculating the new pressure at a higher temperature.

Pressure-Temperature Relationship

The pressure-temperature relationship indicates that as the temperature of a gas increases, its pressure also increases if the volume is constant. This principle is essential for predicting the change in tire pressure as the temperature rises from 24 °C to 49 °C.