Question

In macroscopic and molecular-level terms, describe what will happen to this balloon if temperature increases while pressure remains constant. What will happen if temperature decreases at constant pressure? What will happen if the balloon is taken up to an elevation of 10,000 feet?

Short answer

When temperature increases at constant pressure, the balloon will expand. When temperature decreases at constant pressure, the balloon will contract. If the balloon is taken to an elevation of 10,000 feet, the balloon will also expand due to decreased atmospheric pressure.

Step-by-step solution

Temperature increases at constant pressure

If the pressure remains constant and the temperature of a gas in the balloon increases, the kinetic energy of the gas molecules will also increase causing them to move faster and in turn, collide more often with the walls of the balloon. According to Charles's Law (volume is directly proportional to temperature when pressure is constant), the volume of the balloon will increase to accommodate the increased molecular activity.

Temperature decreases at constant pressure

If the pressure remains constant and the temperature decreases, the kinetic energy of the gas molecules inside the balloon will decrease, causing them to move slower and collide less often with the balloon walls. Again, using Charles's Law, the volume of the balloon will decrease due to less molecular activity.

Change in elevation

If the balloon is taken up to an elevation of 10,000 feet, the external atmospheric pressure decreases because the amount of air above the balloon is less. This results in a lower force applied on the outside of the balloon. With less pressure exerted on it from the outside, the gas molecules inside the balloon will push outwards, causing the balloon to expand. This expansion is described by Boyle’s Law, which states that the volume of a gas increases as the external pressure decreases if the temperature remains constant.

Key concepts

Charles’s Law

Charles's Law is a foundational principle in the study of gas behaviors, stating that for a given mass of gas at constant pressure, the volume is directly proportional to its temperature measured in Kelvins. In simpler terms, if you heat a gas, as long as the pressure doesn't change, the gas will occupy more space. Imagine a balloon being heated; it expands because the air molecules inside move around more vigorously, needing more room to 'dance.' Conversely, if the balloon is cooled, the activity of the molecules slows down, and they take up less space, leading to a smaller balloon.

Here’s how this works mathematically: Charles's Law is usually expressed as \( V \propto T \), or \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \) where \( V \) represents volume, and \( T \) represents temperature. When using this equation, remember that temperature must be in Kelvins, which can be converted from Celsius by adding 273.15.

Kinetic Molecular Theory

The kinetic molecular theory provides a microscopic-level explanation of the behavior of gases. It postulates that gas molecules are constantly in random, straight-line motion and that the temperature of a gas reflects the average kinetic energy of its molecules. When temperature increases, it implies that the molecules move faster because their kinetic energy goes up.

According to this theory, there are a few key points to remember:

• Gas particles are tiny compared to the distances between them.
• The collisions between gas particles are elastic, meaning they don’t lose energy when they collide.
• Gas particles are in continuous, random motion.
• The average kinetic energy of gas molecules is proportional to the absolute temperature of the gas.

Understanding these points helps explain how gases expand when heated and contract when cooled, as observed in Charles's Law and Boyle’s Law.

Boyle’s Law

Boyle's Law is another essential piece of the puzzle in understanding gas behavior, where it states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. If the pressure on a gas increases, the volume decreases, and vice versa.

Let's picture a balloon again, this time being squeezed. As you apply pressure by squeezing, you force the gas molecules into a smaller volume. Conversely, if you release the pressure, the gas expands again. Mathematically, Boyle’s Law can be represented by the equation \( P_1V_1 = P_2V_2 \), where \( P \) is pressure, and \( V \) is volume. This principle is commonly observed when taking a bag of chips to a high-altitude location where the bag puffs up due to lower outside pressure, demonstrating a real-life example of Boyle's Law at work.

Temperature-Pressure Relationship

The temperature-pressure relationship in gases is closely linked to the kinetic molecular theory. As temperature increases, the kinetic energy of gas molecules increases, leading to more frequent and forceful collisions with the container walls. This results in an increase in pressure if the gas volume is constant.

It’s important to note that altitude can also affect this relationship. At higher elevations, like the 10,000 feet mentioned in the exercise, the atmospheric pressure is lower, which can cause an unheated balloon to expand as the external pressure drops.

An understanding of the temperature-pressure relationship is crucial for various practical applications, such as predicting weather patterns, where rising temperature often leads to lower pressure, signaling a change in weather.