Question

Draw a highly magnified view of a sealed, rigid container filled with a gas. Then draw what it would look like if you cooled the gas significantly but kept the temperature above the boiling point of the substance in the container. Also draw what it would look like if you heated the gas significantly. Finally, draw what each situation would look like if you evacuate enough of the gas to decrease the pressure by a factor of 2.

Short answer

In a sealed, rigid container filled with gas, molecules would be distributed randomly with moderate distances between them. Upon cooling the gas significantly (but above its boiling point), the gas molecules would be closer together. When the gas is heated significantly, the molecules would be further apart due to increased kinetic energy. If the gas pressure is decreased by a factor of 2, the molecules would occupy half of the container's volume while maintaining their respective distances for cooled, heated, and initial states.

Step-by-step solution

Drawing the sealed rigid container filled with a gas

Begin by drawing a rectangular sealed container. Inside the container, draw small circles distributed randomly, representing the gas molecules. At this stage, the distance between gas molecules should be moderate, as this is the initial state of the gas in the container.

Drawing the cooled gas (temperature above the boiling point)

Next, draw a similar container with the same dimensions. This time, represent the gas molecules as small circles that are closer together to indicate a lower temperature. Remember that the gas should still be above its boiling point, so don't make them too close together.

Drawing the heated gas

Now, draw another container with the same dimensions. In this container, depict the gas molecules as small circles that are further apart from one another. This signifies that the kinetic energy of the gas molecules has increased due to the higher temperature.

Drawing the container after evacuating half the gas

Starting with the initial state of the gas container, draw a new container with the same dimensions. This time, represent the gas molecules occupying half the volume of the container. The gas molecules should be placed at the same distance as in the initial state, but their quantity should be half that of the initial state.

Drawing the container after evacuating half the gas and cooling

Draw another container with the same dimensions. Depict the gas molecules in the container to represent half the pressure and a lower temperature. The gas molecules should be closer together due to the lower temperature, but still occupy half the volume as in the previous step.

Drawing the container after evacuating half the gas and heating

Lastly, draw a final container with the same dimensions. This time, represent the gas molecules as small circles that are further apart from one another due to the high temperature. However, remember that the pressure is still reduced by half, so ensure that the gas molecules occupy only half the volume of the container.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a crucial formula in understanding how gases behave. It combines several simple gas laws into one. This law relates a gas’s pressure, volume, temperature, and the number of moles, allowing you to predict how changing one factor affects the others. It is represented by the equation: \( PV = nRT \). Here, \( P \) represents pressure, \( V \) stands for volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

This equation shows that pressure and volume are directly proportional to the temperature and the number of moles. When you increase the temperature, either pressure or volume should increase, given the number of moles remains constant. Think of diving deep into a pool. As you go deeper (increasing pressure), your lungs contract (decreasing volume) if temperature stays the same.

Understanding these relationships helps us interpret how gases work in everyday situations, from inflating a balloon to understanding weather patterns.

Molecular Motion

Molecular motion refers to the movement of particles within a substance. In gases, this motion is particularly significant and follows certain key principles. Gas molecules are always in random, fast, and continuous motion. This motion gets faster when heated and slows down when cooled. The speed and movement of these molecules contribute to the gas’s pressure and temperature.

When you imagine a sealed container with gas, these molecules collide with each other and the walls of the container, creating pressure. When you heat the gas, the molecules move faster, hit the walls harder, which increases the pressure if the volume is constant. Conversely, cooling the gas slows down the molecules, lowering the pressure in a fixed volume.

• Faster motion = Higher pressure (increased temperature)
• Slower motion = Lower pressure (decreased temperature)

The findings in experiments where gas molecules are heated or cooled provide insights into how heat energy translates into molecular energy, driving the whole behavior of the gas.

Pressure and Temperature

Pressure and temperature are significant factors in gas behavior. Pressure in gases results from molecular collisions inside a container, and temperature measures the average kinetic energy of these molecules.

When you heat a gas, you increase the kinetic energy of its molecules. This increase results in a higher frequency and force of collisions, thereby raising the pressure when volume remains constant. On the other hand, cooling a gas decreases its molecular motion, leading to fewer collisions and therefore lower pressure.

In practical terms, this can be seen when a sealed balloon is heated—it expands, showing that its internal pressure has increased. If cooled, the balloon shrinks as the internal pressure decreases. Understanding how pressure and temperature are interrelated helps us analyze diverse scenarios, like weather changes, tire pressure variations, and even the behavior of hot air balloons.

Thermodynamics

Thermodynamics involves the study of energy transformations in physical systems. It explains many principles governing temperature, heat, and energy flow within gases. Understanding thermodynamics is key to understanding how gases react with heat.

In thermodynamics, energy as heat either increases the system’s temperature or transforms into work. When heat is added to a gas at a constant volume, it results in an increase in pressure due to greater molecular motion. If a gas undergoes expansion (increasing volume) at constant pressure, it absorbs heat, increasing its internal energy.

• Heat added = Increase in temperature or pressure
• Heat removed = Decrease in temperature or pressure

In everyday life, thermodynamic principles explain why a hot air balloon rises: heated air inside the balloon decreases in density, thus creating lift. By comprehending these basic concepts, engineers and scientists design systems like engines and refrigerators, taking advantage of energy transformations to perform useful work.