If a car tire is filled to a pressure of 32.0 lb/in.2 (psi) measured at 75°F, what will be the tire pressure if the tires heat up to 120°F during driving?

Verified step by step guidance

1. Convert the initial and final temperatures from Fahrenheit to Kelvin using the formula: K = (°F - 32) × \frac{5}{9} + 273.15.
2. Use the ideal gas law in the form of the combined gas law: \frac{P_1}{T_1} = \frac{P_2}{T_2}, where P_1 and T_1 are the initial pressure and temperature, and P_2 and T_2 are the final pressure and temperature.
3. Substitute the initial pressure (P_1 = 32.0 psi) and the converted temperatures (T_1 and T_2) into the combined gas law equation.
4. Solve the equation for the final pressure (P_2) by rearranging it to P_2 = P_1 \times \frac{T_2}{T_1}.
5. Calculate the final pressure using the values obtained from the previous steps.

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. This law implies that for a fixed volume of gas, an increase in temperature will lead to an increase in pressure, assuming the amount of gas remains constant. This principle is crucial for understanding how tire pressure changes with temperature.

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 tire volume does not change significantly, this law helps illustrate the relationship between temperature and pressure, indicating that as temperature increases, pressure also increases in a closed system like a tire.

Pressure-Temperature Relationship

The pressure-temperature relationship in gases indicates that pressure increases with temperature in a closed system. This relationship can be quantified using the formula P1/T1 = P2/T2, where P is pressure and T is temperature in Kelvin. Understanding this relationship allows for the calculation of the new tire pressure after a temperature increase.