Understanding Ideal Gas Law in a Football Game
What are the key factors to consider when determining the amount of heat lost by the air in a football, the gauge pressure of air in the football at the stadium, and the gauge pressure of air at the original inflation?
a) The amount of heat lost by the air in the football can be determined using the ideal gas law, which states that for a fixed amount of gas at constant volume, the pressure is directly proportional to the temperature. Since the volume remains constant at 2500 cm^3, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the amount of gas in moles, R is the gas constant, and T is the temperature in Kelvin. To calculate the amount of heat lost, we need to find the change in temperature between the initial and final states. Converting the temperatures to Kelvin, we have T1 = 15 + 273 = 288 K and T2 = 5 + 273 = 278 K. As the volume is constant, we can rearrange the ideal gas law equation to find the change in pressure: ΔP = (nR/V)ΔT. Plugging in the values, we get ΔP = (nR/2500)ΔT.
b) To determine the gauge pressure of the air in the football at the stadium, we need to consider the new temperature and the initial gauge pressure. Using the ideal gas law equation again, we can find the new pressure by rearranging the equation to P2 = (nR/V)T2. Plugging in the values, we have P2 = (nR/2500)(5 + 273). Subtracting the atmospheric pressure from P2 will give us the gauge pressure at the stadium.
c) To find the initial gauge pressure at which the ball must have been inflated so that it would be equal to 1 bar gauge at the stadium, we can use the ideal gas law equation once again. Rearranging the equation to find the initial pressure, we have P1 = (nR/V)T1. Plugging in the values, we get P1 = (nR/2500)(15 + 273). Subtracting the atmospheric pressure from P1 will give us the gauge pressure at the initial inflation.
The Ideal Gas Law in Football Games
The Ideal Gas Law: The ideal gas law is a fundamental equation in physics and chemistry that describes the behavior of an ideal gas. It relates the pressure, volume, temperature, and amount of gas in a system. In the case of a football game, the ideal gas law can help us understand the changes in pressure and temperature of the air inside the football.
Calculating Heat Lost by the Air
When a football is inflated to a certain pressure and temperature, the air inside it will lose heat as the temperature changes. By using the ideal gas law and the concept of constant volume, we can calculate the amount of heat lost by the air in the football. This calculation is crucial for maintaining the pressure inside the football and ensuring fair play during the game.
Determining Gauge Pressure at Different Temperatures
At the stadium, the air temperature can be significantly different from the initial inflation temperature. This change in temperature will affect the gauge pressure of the air inside the football. By applying the ideal gas law equation and considering the atmospheric pressure, we can determine the gauge pressure at the stadium and the initial inflation pressure needed for the football to reach 1 bar gauge at the stadium.
Conclusion
Understanding the ideal gas law and its application in football games is essential for maintaining the proper pressure inside the football. By considering factors such as temperature, volume, and pressure, we can calculate the amount of heat lost by the air, determine the gauge pressure at different stages of the game, and ensure a fair competition for all players involved.