Problem 15 - Chemistry: An Atoms-Focused Approach

Question

Describe two ways to increase the internal energy of a gas sample.

Step-by-Step Solution

Answer

Answer: The two ways to increase the internal energy of a gas sample are by 1) increasing its temperature and 2) compressing the gas sample.

Step 1: Understand internal energy

Internal energy is the total amount of energy contained in a system, including the kinetic energy of the particles and the potential energy of their interactions. In a gas sample, the internal energy can be represented as the sum of the kinetic energy of the gas molecules. The kinetic energy of the gas molecules depends on their temperature and mass. Hence, temperature plays a crucial role in determining the internal energy of a gas sample.

Step 2: Method 1: Increasing the temperature of the gas sample

One way to increase the internal energy of a gas sample is by increasing its temperature. Temperature is directly proportional to the average kinetic energy of the gas molecules, which means that when the temperature increases, the kinetic energy of the gas molecules also increases. Consequently, this leads to an increase in internal energy. To increase the temperature of the gas sample, you can apply heat externally using a heat source like a flame or a hot plate. As the gas absorbs heat, the energy of its molecules increases, leading to an increase in the internal energy of the gas sample.

Step 3: Method 2: Compression of the gas sample

Another way to increase the internal energy of a gas sample is by compressing the gas. Compression is the process of applying force to decrease the volume of a gas sample. When the volume of a gas sample is reduced, the gas particles are forced to collide more frequently and with greater force, which leads to an increase in the kinetic energy of the gas molecules. To compress the gas sample, you can use a syringe or a piston-cylinder setup. By applying an external force on the piston, the volume of the gas sample will decrease, raising the pressure and the temperature of the gas. This ultimately leads to an increase in the internal energy of the gas sample.

Key Concepts

Understanding Kinetic Energy in Gases

When we discuss the kinetic energy of gases, we're referring to the energy that the gas molecules possess due to their motion. In gases, particles are always moving, and their speed can vary depending on several factors.

• Each molecule in a gas has kinetic energy because it is constantly moving. The faster these molecules move, the greater their kinetic energy.
• The total kinetic energy of the gas is the sum of the kinetic energies of all its molecules.

Kinetic energy is crucial because it directly affects how a gas behaves under different conditions. For instance, when you increase a gas's temperature, its molecules move faster. This increase in speed raises the gas's kinetic energy, which directly increases its internal energy as well. Remember that kinetic energy in gases is not just about speed; it is a reflection of how active the gas molecules are at any given moment.

Role of Temperature in Internal Energy

Temperature is a measure of the average kinetic energy of the particles in a substance. Think of it as an indicator of how energetic the molecules in a gas sample are.

• As you heat a gas, you're increasing the energy of its molecules, making them move faster. This increase translates directly into an increase in temperature.
• High temperature means that gas molecules are moving swiftly, and as a result, have more kinetic energy.

Thus, temperature is directly related to the internal energy of a gas. When you raise the temperature of a gas, you increase its internal energy. This is why heating a gas sample is one effective method to boost its internal energy. It's essential to remember that temperature changes can significantly affect other properties of the gas, such as pressure and volume, according to the ideal gas law.

Understanding Gas Compression

Gas compression involves reducing the volume of the gas by applying external pressure. When you compress a gas, several things happen to its internal energy:

• As the gas is compressed, its particles are squished into a smaller volume. This close proximity forces more frequent and energetic collisions among the molecules.
• These frequent collisions increase the kinetic energy of the gas molecules, thereby increasing the internal energy of the gas.

Compression typically increases the temperature of the gas. This is because when molecules are forced to collide more often, they get more agitated, increasing kinetic energy and thus raising the temperature. To visualize this, imagine using a piston to compress air in a cylinder: as the piston rod pushes down, the air molecules are packed tighter together, leading to higher pressure and temperature, resulting in an increase in internal energy. Thus, compression is a powerful technique to enhance a gas's internal energy.