B.1.1 Understanding thermal energy transfer mechanisms

Molecular Theory of Matter

Molecular Behavior in Solids, Liquids, and Gases

Matter exists in three primary states: solids, liquids, and gases. The behavior of molecules in each state is distinct and is determined by the intermolecular forces and the energy of the particles.

Solids

1. Arrangement: Molecules are tightly packed in a fixed, orderly structure.
2. Movement: Particles vibrate around fixed positions but do not move freely.
3. Forces: Strong intermolecular forces keep particles in place.
4. Properties: Solids have a definite shape and volume.

Liquids

1. Arrangement: Molecules are close together but not in a fixed pattern.
2. Movement: Particles can slide past each other, allowing liquids to flow.
3. Forces: Moderate intermolecular forces allow movement but keep particles relatively close.
4. Properties: Liquids have a definite volume but take the shape of their container.

Gases

1. Arrangement: Molecules are far apart and randomly distributed.
2. Movement: Particles move freely and rapidly in all directions.
3. Forces: Negligible intermolecular forces except during collisions.
4. Properties: Gases have no definite shape or volume and are highly compressible.

Density ($\rho$)

Definition and Calculation

Density is a measure of how much mass is contained in a given volume. It is defined by the formula:

$$\rho =\frac{m}{V}$$

Where:

• $\rho$ = density ($kg{m}^{-3}$)
• $m$ = mass ($kg$)
• $V$ = volume ($m^3$)

Density in Different States of Matter

1. Solids: High density due to tightly packed particles.
2. Liquids: Slightly lower density than solids but still compact.
3. Gases: Very low density because particles are far apart.

Temperature Scales

Celsius and Kelvin Scales

The Celsius and Kelvin scales are two commonly used temperature scales.

• Celsius Scale:
  • Based on the freezing point (0°C) and boiling point (100°C) of water.
• Kelvin Scale:
  • An absolute temperature scale starting at absolute zero (0 K), the lowest possible temperature where molecular motion stops.

Converting Between Celsius and Kelvin

The relationship between the two scales is:

$$T(\text{K})=T(°\text{C})+273$$

Temperature and Average Kinetic Energy

The Connection Between Temperature and Kinetic Energy

1. Temperature is a measure of the average kinetic energy of particles in a substance.
2. In the Kelvin scale, this relationship is direct and proportional.
3. The average kinetic energy ($E_k$) of a particle is given by:

$$E_k=\frac{3}{2}{k}_{B}T$$

where:

• $E_k$ = average kinetic energy (J)
• $k_B$ = Boltzmann constant ($1.38\times {10}^{-23}J{K}^{-1}$)
• $T$ = temperature in Kelvin (K)

Internal Energy

Components of Internal Energy

Internal energy ($U$) is the total energy contained within a system. It consists of two main components:

• Random Kinetic Energy:
  • Due to the motion of particles (translation, rotation, vibration).
• Intermolecular Potential Energy:
  • Due to the forces between particles (attractive or repulsive).

Changes in Internal Energy

Internal energy can change through:

• Heating or Cooling:
  • Adding thermal energy increases kinetic energy.
• Phase Changes:
  • During melting or boiling, potential energy increases as particles move farther apart.
• Work Done on or by the System:
  • Compressing a gas increases its internal energy.

Thermal Energy Transfer Direction

Heat Flow

1. Heat is the energy transferred between two bodies due to a temperature difference.
2. It always flows from regions of higher temperature to regions of lower temperature until thermal equilibrium is reached.

Reflection and Review