Problem 40 - Master Resource Book in JEE Main Physics

Question

Solids expand on heating because (a) kinetic energy of the atoms increases (b) potential energy of the atoms increases (c) total energy of the atoms increases (d) the potential energy curve is asymmetric about the equilibrium distance between neighbouring atoms

Step-by-Step Solution

Answer

(d) the potential energy curve is asymmetric about the equilibrium distance.

Step 1: Understanding Thermal Expansion

Thermal expansion occurs when a solid is heated, leading to an increase in volume. This is because the atoms or molecules within the solid move more vigorously as they gain energy, influencing how they interact with one another.

Step 2: Evaluating Kinetic and Potential Energy

When a solid is heated, the kinetic energy of its atoms increases because the atoms vibrate more intensely. However, increased kinetic energy alone doesn't explain thermal expansion in terms of potential energy changes between atoms.

Step 3: Understanding Potential Energy Curve

The potential energy curve between atoms in a solid is not symmetrical. As atoms vibrate more due to heating, they tend to move further apart on this curve, which is asymmetrical about the equilibrium distance, leading to expansion.

Step 4: Conclusion and Correct Option

The correct explanation for why solids expand on heating is due to the shape of the potential energy curve being asymmetrical. Thus, the most appropriate option is (d), describing the asymmetry about the equilibrium distance.

Key Concepts

Kinetic Energy

Kinetic energy is the energy that an object possesses because of its motion. In the context of thermal expansion, it refers to the energy of atoms or molecules as they move and vibrate. When a solid is heated, its atoms receive more energy from the heat source. This extra energy makes them vibrate faster and more vigorously. Imagine a dance floor getting crowded and lively; as more energy is added in the form of heat, each dancer (or atom) starts moving with more zest.

• The kinetic energy of a body increases with temperature, as the particles move faster.
• In the case of solids, increased kinetic energy results in more significant atomic vibrations.
• This change directly impacts how closely these atoms can pack together, influencing the material's overall volume.

While kinetic energy is a critical component of understanding thermal dynamics in solids, it alone doesn't account for the increase in volume. This is where the potential energy and potential energy curve come into play.

Potential Energy

Potential energy is the stored energy of an object due to its position, arrangement, or state. In the context of atoms within a solid, potential energy is connected to the forces that atoms exert on each other.

As the solid is heated and atoms gain kinetic energy, they oscillate more fiercely about their equilibrium positions. The arrangement affected by these movements is where potential energy plays a key role.

• This energy depends on the distance between atoms; as they move apart, potential energy varies.
• Changes in potential energy influence how atoms are held together, and their existing bonds.

As atoms vibrate due to increased heat, potential energy determines whether the changes in distance involve a stretching or compressing mechanism between atoms. To understand fully why this leads to thermal expansion, the concept of the potential energy curve must also be examined.

Potential Energy Curve

A potential energy curve visually represents the energy of particles depending on their distances. For atoms in a solid, it's like a landscape of hills and valleys showing how potential energy changes as they move relative to one another.

In the phenomenon of thermal expansion, the key factor is the asymmetrical shape of this curve around the equilibrium distance of atoms. This can be imagined as a skewed valley that isn't perfectly symmetrical.

• As atoms vibrate due to increased temperature, they explore more around this asymmetric curve.
• Since the curve is not symmetrical, when atoms gain kinetic energy, they tend to favor moving to positions farther apart.
• This movement leads to an overall increase in average atomic separation, causing expansion in the material.

Thus, while kinetic energy and potential energy contribute to the dynamics inside a solid, it is really the asymmetric nature of this potential energy curve that fundamentally explains thermal expansion.