A Balloon Contains 2.0 L Of Air At 101.5 KPa. You Squeeze The Balloon To A Volume Of 0.5 L. What Is The Pressure Of Air Inside The Balloon?A. 13 KPa B. 101 KPa C. 406 KPa D. 812 KPa

Mar 13, 2025 by ADMIN 185 views

Understanding the Relationship Between Pressure and Volume

In the field of physics, particularly in the study of thermodynamics, understanding the relationship between pressure and volume is crucial. The ideal gas law, which is a fundamental concept in thermodynamics, describes the behavior of ideal gases under various conditions. In this article, we will explore the relationship between pressure and volume using the ideal gas law and apply it to a real-world scenario.

The Ideal Gas Law

The ideal gas law is a mathematical equation that describes the behavior of ideal gases under various conditions. It is expressed as:

PV = nRT

Where:

P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the gas constant
T is the temperature of the gas in Kelvin

Applying the Ideal Gas Law to the Scenario

In the given scenario, we have a balloon containing 2.0 L of air at a pressure of 101.5 kPa. We are asked to find the pressure of the air inside the balloon when it is squeezed to a volume of 0.5 L.

Using the ideal gas law, we can set up the following equation:

P1V1 = P2V2

Where:

P1 is the initial pressure (101.5 kPa)
V1 is the initial volume (2.0 L)
P2 is the final pressure (unknown)
V2 is the final volume (0.5 L)

Solving for the Final Pressure

We can rearrange the equation to solve for the final pressure:

P2 = P1V1 / V2

Substituting the values, we get:

P2 = (101.5 kPa)(2.0 L) / (0.5 L)

P2 = 406 kPa

Therefore, the pressure of the air inside the balloon when it is squeezed to a volume of 0.5 L is 406 kPa.

In conclusion, the ideal gas law provides a powerful tool for understanding the relationship between pressure and volume. By applying the ideal gas law to a real-world scenario, we can determine the final pressure of a gas when its volume is changed. In this article, we used the ideal gas law to find the pressure of the air inside a balloon when it is squeezed to a volume of 0.5 L.

Key Takeaways

The ideal gas law describes the behavior of ideal gases under various conditions.
The ideal gas law is expressed as PV = nRT.
The pressure and volume of a gas are inversely proportional.
The final pressure of a gas can be determined using the ideal gas law.

Frequently Asked Questions

What is the ideal gas law?
How does the ideal gas law relate to pressure and volume?
Can the ideal gas law be used to determine the final pressure of a gas when its volume is changed?

Answers

The ideal gas law is a mathematical equation that describes the behavior of ideal gases under various conditions.
The ideal gas law relates to pressure and volume by describing the inverse proportionality between the two.
Yes, the ideal gas law can be used to determine the final pressure of a gas when its volume is changed.

References

Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
Cengel, Y. A., & Boles, M. A. (2015). Thermodynamics: An Engineering Approach. McGraw-Hill Education.

Additional Resources

Ideal Gas Law Calculator: A calculator that can be used to determine the final pressure of a gas when its volume is changed.
Thermodynamics Tutorial: A tutorial that provides an introduction to thermodynamics and the ideal gas law.
A Balloon Contains 2.0 L of Air at 101.5 kPa. You Squeeze the Balloon to a Volume of 0.5 L. What is the Pressure of Air Inside the Balloon?

Q&A: Understanding the Relationship Between Pressure and Volume

In our previous article, we explored the relationship between pressure and volume using the ideal gas law. We applied the ideal gas law to a real-world scenario and determined the final pressure of a gas when its volume is changed. In this article, we will continue to discuss the relationship between pressure and volume and answer some frequently asked questions.

Q: What is the ideal gas law?

A: The ideal gas law is a mathematical equation that describes the behavior of ideal gases under various conditions. It is expressed as PV = nRT, where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the temperature of the gas in Kelvin.

Q: How does the ideal gas law relate to pressure and volume?

A: The ideal gas law relates to pressure and volume by describing the inverse proportionality between the two. This means that as the volume of a gas increases, its pressure decreases, and as the volume of a gas decreases, its pressure increases.

Q: Can the ideal gas law be used to determine the final pressure of a gas when its volume is changed?

A: Yes, the ideal gas law can be used to determine the final pressure of a gas when its volume is changed. By rearranging the equation, we can solve for the final pressure.

Q: What is the relationship between the initial and final pressures of a gas?

A: The relationship between the initial and final pressures of a gas is described by the equation P1V1 = P2V2, where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.

Q: How can we use the ideal gas law to determine the final pressure of a gas when its volume is changed?

A: We can use the ideal gas law to determine the final pressure of a gas when its volume is changed by rearranging the equation to solve for the final pressure. This can be done by substituting the values of the initial and final volumes and pressures into the equation.

Q: What is the final pressure of a gas when its volume is changed from 2.0 L to 0.5 L at a constant temperature?

A: To determine the final pressure of a gas when its volume is changed from 2.0 L to 0.5 L at a constant temperature, we can use the ideal gas law. By rearranging the equation, we get P2 = P1V1 / V2. Substituting the values, we get P2 = (101.5 kPa)(2.0 L) / (0.5 L) = 406 kPa.

Q: What is the relationship between the initial and final temperatures of a gas?

A: The relationship between the initial and final temperatures of a gas is described by the equation T1V1 = T2V2, where T1 is the initial temperature, V1 is the initial volume, T2 is the final temperature, and V2 is the final volume.

Q: How can we use the ideal gas law to determine the final temperature of a gas when its volume is changed?

A: We can use the ideal gas law to determine the final temperature of a gas when its volume is changed by rearranging the equation to solve for the final temperature. This can be done by substituting the values of the initial and final volumes and temperatures into the equation.

In conclusion, the ideal gas law provides a powerful tool for understanding the relationship between pressure and volume. By applying the ideal gas law to real-world scenarios, we can determine the final pressure and temperature of a gas when its volume is changed. In this article, we answered some frequently asked questions and provided examples of how to use the ideal gas law to determine the final pressure and temperature of a gas.