Problem 25 - Pearson Physics

Question

Relate How is the change in thermal energy related to the work in an adiabatic process?

Step-by-Step Solution

Answer

In an adiabatic process, the change in thermal energy equals the negative of the work done by the system.

Step 1: Understanding an Adiabatic Process

In an adiabatic process, there is no exchange of heat between the system and its surroundings. This means that all the energy changes in the system must come from work being done on or by the system.

Step 2: Applying the First Law of Thermodynamics

The first law of thermodynamics is expressed as \( \Delta U = Q - W \), where \( \Delta U \) is the change in internal energy, \( Q \) is the heat exchanged, and \( W \) is the work done by the system. In an adiabatic process, \( Q = 0 \), so \( \Delta U = -W \).

Step 3: Relating Thermal Energy and Work

In an adiabatic process, since \( \Delta U = -W \), the change in internal energy (which can manifest as thermal energy) is entirely due to the work done on or by the system. The internal energy will increase if work is done on the system and decrease if work is done by the system.

Key Concepts

First Law of Thermodynamics

The first law of thermodynamics is a fundamental principle that helps us understand energy interactions. It states that the total energy in a closed system remains constant, although it can change forms.
This law is often expressed through the equation: \( \Delta U = Q - W \). Here, \( \Delta U \) represents the change in internal energy of the system, \( Q \) is the heat added to the system, and \( W \) is the work done by the system. In adiabatic processes, \( Q = 0 \), which simplifies the equation to \( \Delta U = -W \).

• This equation reflects the conservation of energy.
• Energy within a system can shift between work and internal energy.

Understanding this law is crucial for analyzing energetic interactions in various thermodynamic processes.

Internal Energy

Internal energy is the total energy stored within a system. It's a sum of all kinetic and potential energies of the molecules in the system. During processes, internal energy can change, affecting temperature and phase.
In the context of an adiabatic process, the change in internal energy (\( \Delta U \)) is directly related to the work done on or by the system. If the system does work, its internal energy decreases, whereas if work is done on the system, its internal energy increases.

• Internal energy encompasses both the kinetic and potential energy of particles.
• It plays a critical role in determining the thermodynamic state of a system.

Changes in internal energy are essential to understanding how external actions impact a system on a molecular level.

Thermal Energy

Thermal energy is a form of internal energy associated with the temperature of a system. It results from the motion of molecules, where higher temperatures mean higher molecular speeds and vice versa.
In an adiabatic process, thermal energy changes are solely due to work interactions, as no heat is exchanged. This relationship means the only influencing factor on thermal energy changes is the work done on or by the system.

• Temperature changes are indicative of shifts in thermal energy.
• This energy form is significant in specifying a system's heat content.

The transformation of thermal energy is a critical aspect of adiabatic processes, providing insight into the effects of mechanical work on molecular motion.

Work-Energy Principle

The work-energy principle is a concept that describes how work done on or by a system results in energy changes. This principle is tightly linked to the first law of thermodynamics, especially in adiabatic processes where heat remains constant.
In these cases, the entire shift in energy results from work interactions. According to \( \Delta U = -W \), when work is done on the system, energy increases, raising internal energy or, indirectly, thermal energy.

• The work performed translates to energy changes within a system.
• In adiabatic processes, this is crucial as no heat is exchanged.

The work-energy principle highlights the intricate balance of work and energy within a system, clarifying how mechanical actions impact internal and thermal energies.