Thermal Properties of Matter

10.1 Introduction

In everyday life, we often encounter the concepts of heat and temperature, commonly understood as the hotness or coldness of an object. A kettle with boiling water is indeed hotter than an ice box. Scientific definitions are necessary for precision in measurements. We will explore:

• definitions of temperature and heat
• measurement of temperature
• processes that govern heat flow
• phenomena like thermal expansion, boil and freeze transitions that do not involve temperature changes.

10.2 Temperature and Heat

Temperature is a relative measure of how hot or cold an object is. When two objects are in contact, heat transfers between them until thermal equilibrium is reached, meaning both objects attain the same temperature.
Heat is the form of energy that flows between systems due to a temperature difference. The unit of heat is the joule (J), while temperature is measured in Kelvin (K) or Celsius (°C).

10.3 Measurement of Temperature

Temperature is measured using a thermometer, which takes advantage of properties that change with temperature, such as volume of liquids. For instance, mercury or alcohol thermometers showcase linear expansion with temperature changes. Common fixed points used in thermometry are the ice point (0 °C) and the steam point (100 °C).
The relationship between Celsius and Fahrenheit is expressed as:

• F = (9/5)C + 32
  This helps convert between temperature scales easily.

10.4 Ideal Gas Equation and Absolute Temperature

The behavior of gases can be described by the ideal gas law, which states:

• PV = nRT
  Where P is pressure, V is volume, T is temperature in Kelvin, n is the number of moles, and R is the universal gas constant. At low temperatures, real gases deviate from ideal behavior but the absolute zero is extrapolated to -273.15 °C or 0 K.

10.5 Thermal Expansion

Thermal expansion involves the change in dimensions of an object due to temperature variations.

• Linear expansion is described by: [ \Delta l = \alpha l \Delta T ]
• Area and volume expansions are defined similarly but use coefficients for area and volume respectively. The coefficients of thermal expansion vary according to the material properties and generally, metals have higher expansion coefficients than glass or plastics.

10.6 Specific Heat Capacity

Specific heat capacity (s) is the heat required to raise the temperature of a unit mass of the substance by one degree Celsius:

• s = \frac{Q}{m\Delta T}
  Where Q is heat added, m is mass, and ΔT is the temperature change. Each substance possesses a unique specific heat, influencing applications in temperature modifications.
• Molar specific heat capacity (C) relates to moles, defined as: [ C = \frac{Q}{\mu \Delta T} ]

10.7 Calorimetry

Calorimetry involves measuring the heat transfer in a system. An isolated system without heat exchange features calorimeters that measure how heat is exchanged between substances of different temperatures.
By applying conservation of energy, the heat lost and gained can be quantified during various processes, such as the melting of ice or vaporization of water.

10.8 Change of State

Changes in state (solid, liquid, gas) depend on heat flow:

• Melting occurs as solid changes to liquid at its melting point.
• Boiling occurs at a defined boiling point. The process shows that heat flows without temperature changes during state transitions, hence termed latent heat (L) for phase changes:
• Q = mL
  Where Q is heat and m is mass.
  Latent heat of fusion and latent heat of vaporization indicate the energy needed for phase transitions at constant temperature.

10.9 Heat Transfer

Heat transfer can occur through:

1. Conduction - transfer by physical contact (e.g., heating a metal rod).
2. Convection - transfer through bulk fluid motion (e.g., boiling water).
3. Radiation - transfer through electromagnetic waves (e.g., feeling warmth from the sun).

10.9.1 Conduction

Described by Fourier's law, the heat current H through a material is proportional to the temperature difference and the material's conductivity, expressed as:

• H = K A (T1 - T2) / L
  Where K is thermal conductivity, A is cross-section area, and L is material length.

10.9.2 Convection

Involves fluid movement influenced by temperature gradients. Hot areas rise due to lower densities while cooler areas sink, creating a cycle that transfers heat.

10.9.3 Radiation

Transfers energy through electromagnetic waves, irrespective of matter, allowing heat transfer over vast distances.

10.10 Newton’s Law of Cooling

States the rate of heat loss of a body is proportional to the temperature difference from the surroundings, represented as:

• dQ/dt = -k(T - T1)
  This law allows predictions about cooling or heating processes in various systems, essential for understanding heat transfer dynamics.

1. Heat is energy transferred due to temperature differences.
2. Temperature is a relative measure of hotness.
3. The SI unit of heat is joules (J); for temperature, it is Kelvin (K).
4. Temperature is measured using thermometers that rely on thermometric properties.
5. The ideal gas law relates pressure, volume, and absolute temperature as PV = nRT.
6. Thermal expansion describes changes in dimensions due to temperature changes.
7. Specific heat capacity indicates heat required to change the temperature of a unit mass by 1 °C.
8. Calorimetry measures heat transfer and involves principles of conservation of energy.
9. Heat transfer occurs through conduction, convection, and radiation.
10. Newton's Law of Cooling explains the rate of temperature change based on surrounding temperature differences.