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Chapter 19: Problem 10

Briefly explain thermal expansion using the potential energy-versus- interatomic spacing curve.

Short Answer

Expert verified
In your own words, explain how the potential energy-interatomic spacing curve can be used to describe thermal expansion. The potential energy-interatomic spacing curve can be used to describe thermal expansion by illustrating the relationship between the potential energy of a system and the distance between atoms, or interatomic spacing. When the temperature of a substance increases, the atoms gain kinetic energy and their vibrations become more vigorous. This leads to increased interatomic spacing between atoms, which makes the substance expand. This expansion can be represented on the potential energy-interatomic spacing curve as a shift in the average position of the atoms away from the equilibrium point, causing the entire curve to move upwards. This upward shift demonstrates the increased potential energy due to the expansion of the substance and helps in understanding the correlation between temperature increases, changes in interatomic spacing, and potential energy of the system. Therefore, the potential energy-interatomic spacing curve serves as a useful tool to explain the phenomenon of thermal expansion.

Step by step solution

01

Understand the key concepts

Before explaining thermal expansion using the potential energy interatomic spacing curve, we need to understand a few key concepts: 1. **Thermal Expansion**: It is the increase in the size of the solid, liquid, or gas as a result of an increase in temperature. 2. **Potential Energy**: It is the energy possessed by an object due to its position relative to others or the stored energy in a system of interacting particles. 3. **Interatomic Spacing**: It refers to the distance between atoms in a substance, measured as a function of equilibrium distance. 4. **Potential Energy Curve**: A graph that represents the potential energy of a system as a function of interatomic spacing or distance between particles.
02

Describe the potential energy-interatomic spacing curve

The potential energy-interatomic spacing curve depicts the relationship between the potential energy of atoms in a solid and the distance between them. The curve has a minimum point, which corresponds to the equilibrium position where the potential energy of the system is the lowest. At this position, the attractive and repulsive forces between atoms reach an equilibrium. In general, as the atoms move away from each other (increasing interatomic spacing), the potential energy of the system increases, and as they come closer (decreasing interatomic spacing), the potential energy of the system also increases.
03

Explain the effect of temperature change on interatomic spacing

When the temperature of a substance increases, the kinetic energy of its atoms or particles also increases. This results in an increase in the average amplitude of their vibrations, leading to a higher chance that the atoms will move to a position where the interatomic spacing is larger than the equilibrium distance. As the substance gets hotter, the overall effect is that the substance will occupy a larger volume due to the increased average interatomic spacing between its atoms.
04

Explain how the potential energy-interatomic spacing curve is used to describe thermal expansion

The potential energy-interatomic spacing curve can be used to explain thermal expansion as follows: As the temperature of the substance increases, the atoms gain kinetic energy, causing them to vibrate more. This results in an increased probability of the atoms occupying positions where the interatomic spacing is larger. Consequently, the substance expands as the average separation between atoms increases. On the potential energy curve, this corresponds to a shift in the average position of the atoms away from the equilibrium point, causing the entire curve to shift upwards. This upward shift of the potential energy curve is indicative of an increase in potential energy, which in turn reflects the increase in thermal expansion. By understanding the correlation between temperature increases, changes in average interatomic spacing, and the potential energy between atoms, we can use the potential energy-interatomic spacing curve to effectively explain the phenomenon of thermal expansion.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Potential Energy
Potential energy is a crucial concept in physics, as it refers to the energy stored within a system due to the position or arrangement of its particles. In the context of atoms and molecules, potential energy is related to how particles are positioned relative to one another.
For example, consider two atoms in a solid. They have potential energy because of the forces of attraction (like van der Waals forces or ionic bonds) acting between them when they are close to each other. If you try to bring them much closer than their natural equilibrium position, the potential energy increases because of repulsive forces.
On the other hand, increasing the distance between them until they are too far apart also results in a higher potential energy due to reduced attractive forces. Thus, potential energy plays a key role in determining how atoms interact, bonding, and the structural integrity of materials.
Interatomic Spacing
Interatomic spacing is the distance between the centers of atoms in a substance. It's a critical factor in understanding material behavior and is influenced by temperature, pressure, and other physical conditions. In materials, the equilibrium interatomic spacing is crucial because it reflects a balance between attractive and repulsive forces.
At this equilibrium spacing, the potential energy of the system is minimized, meaning atoms naturally prefer to reside at this distance under stable conditions.
Factors such as increased temperature can lead to changes in interatomic spacing. When the temperature of a substance rises, atoms vibrate more vigorously. This often causes them to move slightly farther apart, resulting in an increased average interatomic spacing, which can lead to the expansion of the material. This concept is fundamental when discussing thermal expansion and structural changes due to temperature variations.
Potential Energy Curve
The potential energy curve is a graphical representation that illustrates how the potential energy of a system changes with respect to the interatomic spacing. This curve typically features a distinct well-shaped dip that signifies the equilibrium position where potential energy is at its lowest.
The curve shows that as atoms are either compressed closer together or stretched farther apart than the equilibrium distance, the potential energy rises due to repulsive and diminished attractive forces, respectively. This graphical tool is invaluable for visualizing how energy is stored within atoms and predicting their behavior under various conditions.
When discussing thermal expansion, the potential energy curve helps illustrate how increased thermal energy (vibration of atoms due to heat) causes a shift in the average position away from the minimum point, leading to expanded interatomic spacing. Understanding the potential energy curve aids in comprehending how materials will react to changes in environmental conditions.

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Most popular questions from this chapter

A \(0.4 \mathrm{m}(15.7 \text { in. })\) rod of a metal elongates \(0.48 \mathrm{mm}(0.019 \text { in. })\) on heating from 20 to \(100^{\circ} \mathrm{C}\left(68 \text { to } 212^{\circ} \mathrm{F}\right) .\) Determine the value of the linear coefficient of thermal expansion for this material.

(a) Briefly explain why \(C_{v}\) rises with increasing temperature at temperatures near \(0 \mathrm{K}\) (b) Briefly explain why \(C_{v}\) becomes virtually independent of temperature at temperatures far removed from \(0 \mathrm{K}\).

(a) Calculate the heat flux through a sheet of brass \(7.5 \mathrm{mm}(0.30 \text { in. })\) thick if the temperatures at the two faces are 150 and \(50^{\circ} \mathrm{C}\) \(\left(302 \text { and } 122^{\circ} \mathrm{F}\right) ;\) assume steady-state heat flow. (b) What is the heat loss per hour if the area of the sheet is \(0.5 \mathrm{m}^{2}\left(5.4 \mathrm{ft}^{2}\right) ?(\mathrm{c}) \mathrm{What}\) will be the heat loss per hour if soda-lime glass instead of brass is used? (d) Calculate the heat loss per hour if brass is used and the thickness is increased to \(15 \mathrm{mm}(0.59 \text { in. })\).

What measures may be taken to reduce the likelihood of thermal shock of a ceramic piece?

We might think of a porous material as being a composite wherein one of the phases is a pore phase. Estimate upper and lower limits for the room- temperature thermal conductivity of an aluminum oxide material having a volume fraction of 0.25 of pores that are filled with still air.
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