A Tire At $21^{\circ} C$ Has A Pressure Of 0.82 Atm. Its Temperature Decreases To $-3.5^{\circ} C$. If There Is No Volume Change In The Tire, What Is The Pressure After The Temperature Change?Use
A Tire's Pressure Change: Understanding the Relationship Between Temperature and Pressure
When it comes to the performance and safety of a vehicle, tire pressure plays a crucial role. A tire that is underinflated can lead to reduced fuel efficiency, uneven tire wear, and even accidents. On the other hand, overinflated tires can be prone to blowouts. Therefore, it is essential to maintain the recommended tire pressure. However, temperature changes can affect the pressure of a tire, which can lead to a decrease in performance and safety. In this article, we will explore the relationship between temperature and pressure in a tire and calculate the pressure change when the temperature decreases.
The behavior of gases, including air in a tire, can be described by the ideal gas law. The ideal gas law states that the product of the pressure (P) and volume (V) of a gas is equal to the product of the number of moles (n) of the gas, the gas constant (R), and the temperature (T) in Kelvin:
P × V = n × R × T
Since we are dealing with a tire, we can assume that the volume remains constant. Therefore, we can rearrange the equation to solve for pressure:
P = n × R × T / V
The ideal gas law shows that pressure is directly proportional to temperature. This means that as the temperature increases, the pressure also increases, and vice versa. This relationship is crucial in understanding how temperature changes affect the pressure of a tire.
Given that the initial temperature of the tire is 21°C and the pressure is 0.82 atm, we can calculate the number of moles of air in the tire using the ideal gas law. However, we need to convert the temperature from Celsius to Kelvin:
T (K) = T (°C) + 273.15 = 21 + 273.15 = 294.15 K
Now, we can use the ideal gas law to calculate the number of moles of air in the tire:
n = P × V / (R × T) = 0.82 atm × V / (0.08206 L atm/mol K × 294.15 K)
However, we are not given the volume of the tire. Since we are told that there is no volume change in the tire, we can assume that the volume remains constant. Therefore, we can use the initial pressure and temperature to calculate the number of moles of air in the tire:
n = P × V / (R × T) = 0.82 atm × V / (0.08206 L atm/mol K × 294.15 K)
Now, we can calculate the pressure after the temperature change. The final temperature is -3.5°C, which is equal to 270.65 K:
P = n × R × T / V = n × 0.08206 L atm/mol K × 270.65 K / V
Since the volume remains constant, we can cancel out the volume term:
P = n × 0.08206 L atm/mol K × 270.65 K / 1 = n × 0.08206 L atm/mol K × 270.65 K
Now, we can substitute the expression for n:
P = (0.82 atm × V / (0.08206 L atm/mol K × 294.15 K)) × 0.08206 L atm/mol K × 270.65 K = 0.82 atm × V / (294.15 K) × 270.65 K = 0.82 atm × V / 1 = 0.82 atm
However, this is the pressure at the initial temperature. We need to calculate the pressure at the final temperature. We can use the ideal gas law to calculate the pressure at the final temperature:
P = n × R × T / V = n × 0.08206 L atm/mol K × 270.65 K / V
Since the volume remains constant, we can cancel out the volume term:
P = n × 0.08206 L atm/mol K × 270.65 K / 1 = n × 0.08206 L atm/mol K × 270.65 K
Now, we can substitute the expression for n:
P = (0.82 atm × V / (0.08206 L atm/mol K × 294.15 K)) × 0.08206 L atm/mol K × 270.65 K = 0.82 atm × V / (294.15 K) × 270.65 K = 0.82 atm × V / 1 = 0.82 atm × (270.65 K / 294.15 K) = 0.82 atm × 0.918 = 0.75 atm
Therefore, the pressure after the temperature change is 0.75 atm.
In conclusion, the pressure of a tire is directly proportional to the temperature. When the temperature decreases, the pressure also decreases. In this article, we calculated the pressure change when the temperature of a tire decreases from 21°C to -3.5°C. We found that the pressure after the temperature change is 0.75 atm. This calculation is essential in understanding how temperature changes affect the performance and safety of a vehicle.
A Tire's Pressure Change: Understanding the Relationship Between Temperature and Pressure - Q&A
In our previous article, we explored the relationship between temperature and pressure in a tire and calculated the pressure change when the temperature decreases. However, we understand that there may be many questions and concerns regarding this topic. In this article, we will address some of the frequently asked questions and provide additional information to help you better understand the relationship between temperature and pressure in a tire.
A: The ideal gas law is a fundamental principle in physics that describes the behavior of gases. It states that the product of the pressure (P) and volume (V) of a gas is equal to the product of the number of moles (n) of the gas, the gas constant (R), and the temperature (T) in Kelvin:
P × V = n × R × T
In the context of a tire, the ideal gas law shows that pressure is directly proportional to temperature. This means that as the temperature increases, the pressure also increases, and vice versa.
A: Maintaining the recommended tire pressure is crucial for the performance and safety of a vehicle. Underinflated tires can lead to reduced fuel efficiency, uneven tire wear, and even accidents. On the other hand, overinflated tires can be prone to blowouts. Therefore, it is essential to check the tire pressure regularly and adjust it according to the manufacturer's recommendations.
A: Temperature changes can affect the pressure of a tire. As the temperature increases, the pressure also increases, and vice versa. This is because the molecules of the gas inside the tire move faster and spread out, increasing the pressure. Conversely, as the temperature decreases, the pressure also decreases, and the molecules of the gas move slower and come together, decreasing the pressure.
A: Yes, you can use a tire pressure gauge to measure the pressure of a tire at different temperatures. However, it is essential to note that the gauge may not provide accurate readings if the temperature is significantly different from the temperature at which the gauge was calibrated.
A: To calculate the pressure change in a tire due to temperature changes, you can use the ideal gas law. The ideal gas law states that the product of the pressure (P) and volume (V) of a gas is equal to the product of the number of moles (n) of the gas, the gas constant (R), and the temperature (T) in Kelvin:
P × V = n × R × T
You can rearrange this equation to solve for pressure:
P = n × R × T / V
Since the volume remains constant, you can cancel out the volume term:
P = n × R × T / 1 = n × R × T
Now, you can substitute the expression for n:
n = P × V / (R × T)
Substituting this expression for n into the equation for pressure, you get:
P = (P × V / (R × T)) × R × T = P × V / (R × T) × R × T = P
Therefore, the pressure is directly proportional to the temperature.
A: The recommended tire pressure for your vehicle can be found in the owner's manual or on the tire information placard on the driver's side doorjamb. It is essential to check the tire pressure regularly and adjust it according to the manufacturer's recommendations.
In conclusion, the relationship between temperature and pressure in a tire is a complex topic that requires a thorough understanding of the ideal gas law. By understanding how temperature changes affect tire pressure, you can ensure that your vehicle is running safely and efficiently. We hope that this Q&A article has provided you with the information you need to better understand this topic. If you have any further questions or concerns, please do not hesitate to contact us.