Problem 70 - Chemistry and Chemical Reactivity

Question

You have a large balloon containing 1.0 mol of gaseous water vapor at \(80^{\circ} \mathrm{C}\). How will each step affect the internal energy of the system? (a) The temperature of the system is raised to \(90^{\circ} \mathrm{C}\) (b) The vapor is condensed to a liquid, at \(40^{\circ} \mathrm{C}.\)

Step-by-Step Solution

Answer

(a) Internal energy increases. (b) Internal energy decreases.

Step 1: Understanding Internal Energy

The internal energy of a system is related to the kinetic and potential energies of the molecules. For a gas, it primarily depends on its temperature, meaning any increase or decrease in temperature will change the internal energy.

Step (a): Effect of Temperature Increase

Raising the temperature from \(80^{\circ}\)C to \(90^{\circ}\)C increases the average kinetic energy of water vapor molecules, leading to an increase in the internal energy of the system.

Step (b): Vapor Condensation

Condensing gaseous water vapor to a liquid at \(40^{\circ}\)C involves a phase change, which releases energy as heat. This transition results in a decrease in the internal energy due to the release of latent heat, coupled with the additional cooling effect from the fall in temperature.

Key Concepts

Internal Energy

Internal energy is a concept that describes the total energy contained within a system's molecules. This energy includes both kinetic energy, which comes from the motion of molecules, and potential energy, which is related to the forces between particles. In the case of gases, internal energy is predominantly influenced by temperature. When the temperature of a gas increases, its molecules move faster. This indicates that their kinetic energy—and thus the internal energy—increases. Conversely, decreasing temperature will result in a lower internal energy because the molecular motion slows down. Understanding these dynamics helps in predicting changes in internal energy when a system undergoes temperature variations or other processes.

Phase Change

A phase change involves a transition between different states of matter, such as from gas to liquid. These transformations occur at constant temperature and involve energy exchanges without a change in the chemical composition of the substance. When gaseous water vapor condenses into a liquid, it undergoes a phase change known as condensation. During this process, the system releases a significant amount of energy in the form of heat, known as latent heat. The release of this energy reduces the internal energy of the system, as the kinetic energy associates more with the liquid state being lower compared to the gaseous state. This highlights the important relationship between phase changes and energy balance within thermodynamic systems.

Kinetic Energy

Kinetic energy is the energy of motion. It's a fundamental aspect of thermodynamics because it helps explain temperature relationships. The molecules in a substance are always moving, and their speed determines the substance's kinetic energy and thus its temperature. In the context of gases such as water vapor, increased temperature results in increased molecular speed and kinetic energy. When the temperature of the gaseous water vapor in the balloon is increased from 80°C to 90°C, this leads to increased kinetic energy of the molecules. This rise in kinetic energy corresponds to an increase in the system's internal energy, showing how closely kinetic energy and temperature are linked.

Heat Transfer

Heat transfer is a process through which thermal energy is exchanged between different bodies or regions of space due to temperature differences. In a system, heat can be added or removed, causing changes in state and temperature. For instance, when the gaseous water vapor is condensed into liquid, heat energy is released from the system into the surroundings. This process is essential in controlling the temperature and phase changes within a system. It is important to understand that heat transfer occurs in three ways: conduction, convection, and radiation. In phase changes like condensation, the energy exchange plays a crucial role in altering the internal energy of the system. Understanding these modes of heat transfer can help determine how energy is distributed when a system undergoes various thermodynamic processes.