Conceptual Physics Practice Page Chapter 14 Gases Gas Pressure Answers

Conceptual Physics Practice Page Chapter 14: Gases, Gas Pressure – Answers and Explanations

This comprehensive guide provides detailed answers and explanations for the practice problems found in Chapter 14 of Paul Hewitt's Conceptual Physics. We'll delve into the core concepts of gases, gas pressure, and related phenomena, ensuring a thorough understanding of this crucial chapter. Remember that understanding the why behind the answers is just as important, if not more so, than simply knowing the correct numerical result.

Understanding Gas Pressure: The Basics

Before we dive into the specific problems, let's review the fundamental principles governing gas pressure. Gas pressure arises from the constant, random motion of gas molecules. These molecules collide with the walls of their container, exerting a force. Pressure is defined as force per unit area:

Pressure = Force / Area

The more frequent and forceful these collisions, the higher the pressure. Several factors influence gas pressure:

• Temperature: Higher temperatures mean faster-moving molecules, leading to more frequent and forceful collisions and thus higher pressure.
• Volume: A smaller volume confines the molecules to a smaller space, increasing the frequency of collisions and therefore the pressure.
• Number of Molecules: More molecules mean more collisions, resulting in higher pressure.

These relationships are formalized in the Ideal Gas Law (though not explicitly covered in a purely conceptual treatment), which states: PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. While we won't be using this equation directly, understanding its implications is crucial to comprehending the behavior of gases.

Practice Problems and Detailed Solutions

Let's now tackle some sample problems that represent the types of questions you might encounter in Chapter 14. Note that without the specific problems from your textbook, I will create examples that mirror the style and difficulty. Remember to always refer to your textbook for the actual questions.

Problem 1: The Relationship Between Temperature and Pressure

Question: A sealed container of gas is heated. Explain what happens to the pressure inside the container and why.

Answer: Heating the gas increases its temperature. This causes the gas molecules to move faster. The faster-moving molecules collide with the container walls more frequently and with greater force. This increase in the frequency and force of collisions results in a higher gas pressure inside the sealed container.

Problem 2: The Relationship Between Volume and Pressure (Boyle's Law)

Question: A balloon is filled with air and then squeezed. Explain what happens to the pressure of the air inside the balloon and why.

Answer: Squeezing the balloon decreases its volume. The same number of air molecules are now confined to a smaller space. This leads to a higher frequency of collisions between the air molecules and the balloon's walls. The increase in collision frequency results in a higher pressure inside the balloon. This illustrates Boyle's Law: at a constant temperature, the pressure of a gas is inversely proportional to its volume (P1V1 = P2V2).

Problem 3: Understanding Atmospheric Pressure

Question: Why does atmospheric pressure decrease with increasing altitude?

Answer: Atmospheric pressure is caused by the weight of the air above a given point. As you go higher in altitude, there is less air above you, hence less weight pushing down. Therefore, atmospheric pressure decreases as altitude increases.

Problem 4: The Effect of Altitude on Boiling Point

Question: Explain why water boils at a lower temperature at higher altitudes.

Answer: The boiling point of water is the temperature at which its vapor pressure equals the surrounding atmospheric pressure. Since atmospheric pressure decreases with increasing altitude, the water needs to reach a lower temperature for its vapor pressure to equal the lower atmospheric pressure. Hence, water boils at a lower temperature at higher altitudes.

Problem 5: Pressure in Different Shaped Containers

Question: Two identical containers, one cylindrical and one spherical, hold the same amount of gas at the same temperature. Do they exert the same pressure? Explain.

Answer: Yes, they exert the same pressure. The pressure exerted by a gas depends on the number of molecules, their temperature, and the volume of the container (not the shape). Since the containers hold the same amount of gas at the same temperature and have the same volume, the frequency and force of collisions with the container walls will be the same, resulting in equal pressures. The shape of the container is irrelevant to the overall pressure exerted by the gas.

Problem 6: Gas Pressure and Molecular Motion

Question: Explain how the speed of gas molecules relates to the pressure they exert.

Answer: The speed of gas molecules is directly related to their kinetic energy. Faster-moving molecules possess higher kinetic energy. These faster molecules collide with the container walls more frequently and with greater force. This increased frequency and force of collisions directly translates to a higher gas pressure.

Problem 7: A More Complex Scenario

Question: A rigid container holds a gas at a certain temperature and pressure. If you add more gas to the container without changing the temperature or volume, what happens to the pressure? Explain using kinetic molecular theory.

Answer: Adding more gas to the container without changing the volume or temperature will increase the pressure. According to the kinetic molecular theory, the pressure of a gas is directly proportional to the number of molecules present. More gas molecules means more collisions with the container walls per unit of time. Since the volume is constant, these increased collisions translate directly into higher pressure.

Problem 8: Applications of Gas Pressure

Question: How does understanding gas pressure help us design things like balloons, tires, and weather forecasting systems?

Answer: Understanding gas pressure is crucial in numerous applications:

• Balloons: The pressure difference between the inside and outside of a balloon allows it to inflate and float. Controlling the amount of gas and its temperature directly impacts the pressure, hence the balloon's size and buoyancy.

• Tires: The air pressure in tires provides the necessary support for vehicles. Maintaining correct tire pressure ensures optimal performance and safety.

• Weather Forecasting: Atmospheric pressure variations are crucial for weather prediction. Changes in pressure indicate changes in weather patterns, helping meteorologists forecast storms, rain, and other weather phenomena.

Going Beyond the Basics: Advanced Concepts

While Conceptual Physics focuses on the fundamental principles, it's beneficial to briefly touch upon more advanced concepts that build upon this foundation:

• Partial Pressures (Dalton's Law): When multiple gases are present in a container, each gas exerts its own pressure, and the total pressure is the sum of these partial pressures.

• Diffusion and Effusion: These describe the movement of gases from high to low concentration areas and the rate of their passage through small openings, respectively. Both phenomena are highly dependent on the mass and velocity of gas molecules.

• Real Gases vs. Ideal Gases: The Ideal Gas Law provides a good approximation for many gases, but real gases deviate from ideality at high pressures and low temperatures due to intermolecular forces and molecular volume.

Conclusion

Mastering the concepts in Chapter 14 of Conceptual Physics requires a strong grasp of the fundamental relationship between temperature, pressure, volume, and the number of molecules. By carefully analyzing the problems and understanding the underlying principles, you'll develop a solid foundation in gas behavior and its various applications in the world around us. Remember to consult your textbook for the exact questions and to use this guide as a supplementary resource for deeper understanding and improved problem-solving skills. Practice consistently, and you will surely master the concepts presented in this chapter.