Pressure of a Bicycle Tire Calculation When Heated

How to calculate the pressure in a bicycle tire when heated?

A bicycle tire is inflated to a pressure of 4.47 atm at 18°C. The tire is then heated to 44°C. What is the pressure in the tire after heating?

Answer:

The pressure in the tire after heating is approximately 5.20 atm, so the correct option is B) 5.20 atm.

When a gas is heated, its temperature and pressure are directly proportional under constant volume conditions, as described by Gay-Lussac's Law. In this scenario, the initial pressure (P1) of the bicycle tire is 4.47 atm at 18°C, which needs to be converted to Kelvin by adding 273.15 (18°C + 273.15 = 291.15 K). The tire is heated to 44°C, which is converted to Kelvin as 44°C + 273.15 = 317.15 K.

Using the formula P1/T1 = P2/T2, where P1 and P2 are the initial and final pressures, and T1 and T2 are the initial and final temperatures, we can calculate the final pressure (P2). By substituting the given values into the formula, we find that the pressure in the tire after heating is approximately 5.20 atm.

Therefore, it is important to consider the relationship between temperature and pressure when dealing with gases, especially in situations where heating or cooling occurs.