Problem 60 - Pearson Physics

Question

The pressure of a system is held fixed. Is it possible for the thermal energy of the system to change? Give an explanation if your answer is no. If your answer is yes, give a specific example.

Step-by-Step Solution

Answer

Yes, thermal energy can change at constant pressure, such as a gas expanding in a cylinder when heated.

Step 1: Understanding the Problem

We need to determine if the thermal energy of a system can change while the pressure remains constant. Thermal energy refers to the internal energy present in the system due to the motion of particles, and altering this energy often involves changes in temperature, volume, or state.

Step 2: Analyzing the Relationship Between Thermal Energy and Pressure

Thermal energy changes can occur through heat transfer or work done by/to the system. At constant pressure, changes in volume can still happen, leading to changes in internal energy.

Step 3: Applying the First Law of Thermodynamics

The first law of thermodynamics states: \( \Delta U = Q - W \), where \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system. At constant pressure, work is \( P \Delta V \), which indicates that changes in internal energy (thermal energy) can occur if there is heat exchange or volume change.

Step 4: Providing an Example

Consider a gas heated in a piston-cylinder assembly at constant pressure. As it absorbs heat, the gas expands, increasing the volume, but the pressure remains constant. This leads to an increase in thermal energy as heat is absorbed.

Key Concepts

Thermal Energy

Thermal energy is essentially the aggregate of the kinetic and potential energies of particles within a system. It is the energy that comes from the motion of these particles. The faster the particles move, the higher the temperature and the greater the thermal energy of the system. This energy plays a key role in understanding how heat impacts physical systems.
When thermal energy changes, it often accompanies shifts in temperature or phase, such as solid to liquid transformation or liquid to gas. The change in thermal energy implies that the internal energy of a system is changing, possibly due to heat transfer, which might involve either adding or removing heat from the system.

• Heat transfer can alter thermal energy without necessarily changing pressure.
• For gases, thermal energy changes can prompt expansions or contractions in volume, influencing how a system behaves at constant pressure.

Pressure

Pressure is the force applied per unit area on the surface of an object. It plays a crucial role in thermodynamics when discussing gases and liquids. In many scenarios, particularly involving gases, pressure stays constant even when other properties, like volume, change.
In terms of a gas in a confined space, constant pressure is often maintained by allowing the system to expand or contract. This balance enables volume changes while keeping pressure the same. Understanding this balance helps explain how internal energy can change even if there is no change in pressure.

• Constant pressure scenarios are common in processes like heating a gas in a piston.
• Pressure's relationship with volume and temperature is crucial for determining how a system's energy can change without altering pressure.

First Law of Thermodynamics

The first law of thermodynamics is a principle centered around energy conservation. The law states that the change in internal energy (\( \Delta U \)) of a system is equal to the heat added to the system (\( Q \)) minus the work done by the system (\( W \)).This can be mathematically expressed as:\[\Delta U = Q - W\]At constant pressure, the work done by the system is defined as \( P \Delta V \), showing that any alterations in volume can lead to changes in internal energy.
This law confirms that even when pressure is constant, as long as there is heat exchange or a change in volume, the system’s thermal energy can change. It serves as a foundation for understanding how energy transfer affects the behaviour and state of matter. It helps predict an outcome when a system's components, such as temperature, pressure, or volume, are altered.

• The principle demonstrates the role of external heat and work in energy fluctuations.
• In thermodynamic processes, both heating and doing work can result in energy changes while maintaining constant pressure.