Problem 23 - Chemistry The Central Science

Question

(a) According to the first law of thermodynamics, what quantity is conserved? (b) What is meant by the internal energy of a system? (c) By what means can the internal energy of a closed system increase?

Step-by-Step Solution

Answer

(a) The conserved quantity in the first law of thermodynamics is the total energy (including internal energy, work, and heat) of the isolated system. (b) Internal energy is the energy associated with the microscopic components of a system, including kinetic and potential energy of atoms and molecules. (c) The internal energy of a closed system can increase through heat transfer from an external source or by mechanical work done on the system.

Step 1: a) Determine the conserved quantity in the first law of thermodynamics

According to the first law of thermodynamics, energy can neither be created nor destroyed, but it can only be transformed from one form to another in an isolated system. This law is essentially the conservation of energy principle. So, the conserved quantity in the first law of thermodynamics is the total energy (including internal energy, work done by or on the system, and heat exchanged) of the isolated system.

Step 2: b) Define internal energy of a system

The internal energy of a system refers to the energy that is associated with the microscopic components (atoms and molecules) of the system. It includes the kinetic energy (energy of motion) and potential energy (energy due to position or interactions) of the microscopic particles in the system. Internal energy is often considered as a function of temperature, volume, and the number of particles within the system.

Step 3: c) Identify the means to increase the internal energy of a closed system

There are two main means by which the internal energy of a closed system can increase: 1. Heat transfer: If heat is transferred to the system from an external source, the internal energy of the system will increase as the temperature of the system rises. 2. Work done on the system: If mechanical work is done on the system, the internal energy of the system increases as the energy is transferred to internal energy. For example, if a piston compresses a gas inside a cylinder, the temperature of the gas increases, and so does the internal energy of the system.

Key Concepts

Conservation of Energy

The principle of conservation of energy is the foundation of the first law of thermodynamics. It states that energy can neither be created nor destroyed, but it can change forms. Think of it like money in a piggybank. You can't magically create more, but you can move it around. In an isolated system, the total energy remains constant, including:

• Internal energy – the energy trapped within the system.
• Heat – energy transferred due to temperature differences.
• Work – energy needed to move things around.

Any changes in one form lead to equal changes in another, maintaining the total energy balance. Understanding this concept helps us grasp how energy flows and transforms in various systems.

Internal Energy

Internal energy is a vital concept in understanding how systems function at a microscopic level. It refers to the total energy contained within a system due to the motion and interactions of its tiny particles, like atoms and molecules. Imagine shaking a can of soda. Each bubble represents atoms or molecules moving around and colliding inside. Internal energy is influenced by several factors, including:

• Temperature – Higher temperature means more energetic particles and thus more internal energy.
• Volume – Changing the volume can affect particle interactions and energy levels.
• Number of particles – More particles mean more total energy.

All these factors play a role in the nature of internal energy, making it a crucial aspect of thermodynamic studies.

Heat Transfer

Heat transfer is a major way the internal energy in a system changes. Think of it as a gift exchange, where energy moves from one part to another. There are three main methods of heat transfer:

• Conduction – Energy passing through materials like heat traveling up a metal spoon.
• Convection – Energy circulating within fluids, like warm air rising and cool air sinking.
• Radiation – Energy traveling in waves, such as the heat felt from the sun.

By absorbing heat, a system's internal energy increases. Conversely, losing heat decreases internal energy. These exchanges are natural outcomes of energy flowing from warmer to cooler areas, seeking equilibrium.

Work Done on a System

Work done on a system is another key way to change its internal energy. Imagine pushing on a box. The effort you put in is analogous to work, transferring energy into the box. In thermodynamics, work can occur in several scenarios:

• Pistons compressing gas in a cylinder, similar to a car engine. Energy is transferred by force.
• Electric currents driving machinery, transforming electrical energy into mechanical energy.
• Gravity acting on objects, where potential energy converts to kinetic energy.

Through work, systems gain energy which increases internal energy, affecting their temperature, pressure, or other properties. This makes understanding work a cornerstone of energy interaction and transformation.