Question

You have a gas in a container fitted with a piston and you change one of the conditions of the gas such that a change takes place, as shown below: State three distinct changes you can make to accomplish this, and explain why each would work.

Short answer

Three distinct changes that can be made are: 1. Changing the Temperature: Increasing or decreasing the temperature of the gas will affect its pressure and volume, according to the ideal gas law (PV=nRT). Hence, higher temperature results in higher pressure and volume, while lower temperature results in lower pressure and volume. 2. Changing the Pressure: Applying or removing external pressure on the piston affects the pressure and volume of the gas inside the container. Additional pressure compresses the gas, while removing pressure allows the gas to expand. 3. Changing the Amount of Gas: Adding or removing gas molecules inside the container will alter the pressure and volume according to the ideal gas law (PV=nRT). Adding gas increases pressure and volume, while removing gas reduces pressure and volume.

Step-by-step solution

1. Changing the Temperature

Increase or decrease the temperature of the gas. According to the ideal gas law (PV=nRT), the relationship between the pressure (P), volume (V), and temperature (T) is directly proportional, assuming the number of gas molecules (n) and the ideal gas constant (R) remain constant. If the temperature is increased, the kinetic energy of the gas molecules will also increase, causing them to move faster and collide more forcefully with the walls of the container, resulting in an increase in pressure. Consequently, the piston will be pushed outwards, increasing the volume of the container. Conversely, if the temperature is decreased, the pressure and volume of the container will also decrease.

2. Changing the Pressure

Apply or remove external pressure on the piston. By applying additional external pressure to the piston, the gas inside the container will be compressed, causing an increase in pressure (P) and a decrease in volume (V), as seen in the ideal gas law (PV=nRT). If enough pressure is applied, the piston will be pushed into the container, reducing its volume. When the external pressure is removed or reduced, the gas will expand, decreasing the pressure inside the container and causing the piston to move outwards, increasing the volume of the container.

3. Changing the Amount of Gas

Add or remove gas molecules inside the container. By adding more gas (increasing the value of n) to the container, the gas pressure inside the container will increase because the total number of collisions of the gas particles with the walls of the container will increase. As a result, the piston will be pushed outwards, increasing the volume of the container, as seen in the ideal gas law (PV=nRT). Conversely, by removing gas molecules from the container, the pressure inside the container will decrease, resulting in a decrease in volume as the piston moves inward.

Key concepts

Gas Dynamics

Gas dynamics studies how gases move and behave, particularly under varying conditions like pressure and temperature. This field of physics helps us understand the motion of gas molecules when subjected to different external and internal changes. The behavior of gases is crucial in many applications, from automobile engines to spacecraft design.

Some key points in gas dynamics include:

• The speed and direction of gas molecules.
• The effects of pressure and temperature on gas movement.
• How gas flow affects surrounding objects.

The molecules in a gas move randomly and collide with each other and the container's walls. When you apply concepts from gas dynamics, you can predict and manipulate the behavior of gases in various scenarios, such as when the gas is compressed or expanded. Understanding gas dynamics is essential when dealing with engines, where the flow and compression of air-gasoline mixtures critically affect performance.

Thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, and the internal energy of systems. It explains how energy is transferred within systems and surroundings. Thermodynamics plays a crucial role in understanding how gases behave under different changes in their environment.

Some basic concepts of thermodynamics include:

• Energy transfer: how energy moves from one place or form to another.
• The laws of thermodynamics, which include principles governing these energy transformations.
• Equilibrium, where a system has no gradient in temperature or pressure across it.

When you change the temperature, pressure, or volume of a gas, thermodynamics helps predict how these changes will affect the gas's behavior. For instance, when you increase the temperature of a gas, the kinetic energy of its particles increases, resulting in increased pressure or volume. By understanding thermodynamics, you can effectively control processes like heating, compressing, and expanding gases.

Boyle's Law

Boyle's Law describes the inverse relationship between the pressure and volume of a gas at a constant temperature. It's a principle in gas laws that helps us understand how gases compress and expand.

The formula for Boyle's Law is:\[ P_1 V_1 = P_2 V_2 \]where \(P_1\) and \(V_1\) are the initial pressure and volume, while \(P_2\) and \(V_2\) are the new pressure and volume. Here's how Boyle’s Law works:

• If you increase the pressure on a gas, its volume decreases.
• If the pressure decreases, the gas expands, and its volume increases.
• Temperature remains constant during these changes.

This law is particularly useful when understanding processes like gas compression in cylinders or breathing mechanics in the respiratory system.

Charles's Law

Charles's Law explains the direct relationship between the volume and temperature of a gas, maintaining constant pressure. This law helps clarify how gases expand when heated.

The formula governing Charles's Law is:\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]where \(V_1\) and \(T_1\) are the initial volume and temperature, and \(V_2\) and \(T_2\) are the final volume and temperature. In this context:

• If the temperature of a gas increases, its volume also increases.
• If the temperature decreases, the volume decreases too.
• Pressure is kept constant in these scenarios.

Charles’s Law is vital in everyday applications like hot air balloons, which rise because the heated air inside makes the balloon lighter than the cooler air outside. Understanding this principle helps manage processes involving temperature changes in gases to predict volume outcomes accurately.