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?

Short answer

(a) According to the first law of thermodynamics, energy is conserved in a closed system. (b) The internal energy of a system is the total kinetic and potential energies of its microscopic particles (atoms, molecules), mainly due to their motion and interactions. (c) The internal energy of a closed system can be increased by (1) adding heat (Q) to the system, and (2) doing work (W) on the system, both of which can be represented in the equation \( ΔE_\text{internal} = Q - W \).

Step-by-step solution

Answering (a) - Identifying the conserved quantity according to the first law of thermodynamics

The first law of thermodynamics states that the energy in a closed system is conserved, meaning that the total energy cannot be created nor destroyed. Mathematically, the first law of thermodynamics can be expressed as: \[ΔE_\text{internal} = Q - W,\] where \( ΔE_\text{internal} \) is the change in the system's internal energy, \( Q \) is the heat added to or removed from the system, and \( W \) represents the work done on or by the system.

Answering (b) - Explaining the internal energy of a system

The internal energy of a system is the total of all kinetic and potential energies associated with the microscopic particles (like atoms or molecules) of the system. These microscopic particles are in constant motion and interact with each other, resulting in the kinetic and potential energies present within the system. The internal energy is a measure of the system's energy required to maintain these microscopic motions and interactions. It may change due to heat transfer, work being done on or by the system, or internal processes (like chemical reactions).

Answering (c) - Ways to increase the internal energy of a closed system

The internal energy of a closed system can be increased mainly through two means: 1. Adding heat (Q): When heat is added to the closed system, the energy transfer increases the microscopic motions and the interactions among the particles in the system, thus increasing the internal energy. According to the first law of thermodynamics, this increase can be represented by a positive value for Q in the equation \( ΔE_\text{internal} = Q - W \). 2. Doing work on the system (W): When work is done on (or received by) the system, it increases the system's energy. For instance, if we compress a gas in a closed container, we are doing work on the system, and this energy transfer can subsequently cause an increase in the internal energy. To represent a positive increase in internal energy due to work done on the system, W should be negative in the equation \( ΔE_\text{internal} = Q - W \), as it is defined as the work done by the system.

Key concepts

Internal Energy

Internal energy is the sum of all the microscopic kinetic and potential energies in a system.
Think of it as the energy contained within the particles like atoms and molecules. These particles are always moving, vibrating, and interacting with one another.
This constant activity gives rise to the system's internal energy.

• Kinetic Energy: The energy due to the motion of particles.
• Potential Energy: The energy from the forces between particles.

Internal energy can change through heat transfer, work, or internal processes, demonstrating its dynamic nature. For example, when a substance is heated, the molecules move faster and interact more energetically, thus increasing its internal energy.

Closed System

A closed system doesn't exchange matter with its surroundings, but it can exchange energy, such as heat and work.
This concept is crucial when studying energy interactions according to thermodynamics.

• No Matter Transfer: No mass enters or leaves the system.
• Energy Transfer: Energy can enter or leave as heat or work.

Whenever you have processes like heating or doing work on a gas in a sealed container, you're dealing with a closed system. By focusing on energy exchanges, we can predict how the system will behave without considering changes in mass.

Energy Conservation

The first law of thermodynamics captures the principle of energy conservation in closed systems.
It tells us that energy cannot be created or destroyed, only transformed or transferred.The mathematical expression is given by: \[ΔE_\text{internal} = Q - W\]

• \( Q \): Heat added to the system increases internal energy.
• \( W \): Work done by the system reduces internal energy.

This equation shows us how purely energy flows influence internal energy:- Adding heat raises internal energy.- Doing work on the system also boosts internal energy.Recognizing the balance of energy transfers helps in understanding and applying the law to real-world scenarios.