Thermal Properties of Matter
How heat flows, why things expand, and what happens when matter changes state
Table of Contents
10.1 Introduction
We all have common sense notions of heat and temperature. Temperature is a measure of 'hotness' of a body. A kettle with boiling water is hotter than a box containing ice. In this chapter, you will learn what heat is and how it is measured, and study the various processes by which heat flows from one body to another.
10.2 Temperature and Heat
Temperature is a relative measure, or indication of hotness or coldness. Heat is the form of energy transferred between two (or more) systems or a system and its surroundings by virtue of temperature difference.
Temperature measures the average kinetic energy of molecules. Heat is energy in transit — it flows from hot to cold. A body doesn't "contain" heat; it contains internal energy. Heat is the energy transferred due to temperature difference.
10.3 Measurement of Temperature
A common thermometer uses the thermal expansion of liquids (mercury or alcohol). The three common scales are:
| Scale | Freezing Point | Boiling Point | Conversion |
|---|---|---|---|
| Celsius (°C) | 0°C | 100°C | °C = K − 273.15 |
| Kelvin (K) | 273.15 K | 373.15 K | K = °C + 273.15 |
| Fahrenheit (°F) | 32°F | 212°F | °F = 9/5(°C) + 32 |
The lowest possible temperature is 0 K = −273.15°C, called absolute zero. At this temperature, molecular motion theoretically stops. The Kelvin scale starts from absolute zero, making it the absolute temperature scale.
10.4 Ideal-Gas Equation and Absolute Temperature
The behavior of ideal gases is described by combining three gas laws:
This equation relates the state variables of an ideal gas. Real gases obey this equation approximately at low pressures and high temperatures.
10.5 Thermal Expansion
Most materials expand when heated. The expansion can be described in three ways depending on the dimension:
Linear Expansion (1D)
ΔL = L₀αΔT
α = coefficient of linear expansion. Applies to rods, wires, rails.
Superficial Expansion (2D)
ΔA = A₀βΔT, where β = 2α
Applies to sheets, plates, surfaces.
Volumetric Expansion (3D)
ΔV = V₀γΔT, where γ = 3α
Applies to liquids, gases, solids in all dimensions.
Anomalous Expansion of Water
Water contracts when heated from 0°C to 4°C, then expands normally above 4°C. Maximum density at 4°C.
Gaps in railway tracks: Expansion gaps prevent buckling in summer. Power lines: Sag more in summer. Bimetallic strips: Used in thermostats — two metals with different α bend when heated.
10.6 Specific Heat Capacity
The amount of heat required to raise the temperature of unit mass of a substance by 1°C (or 1 K) is called its specific heat capacity (c).
Molar specific heat (C) is heat per mole per degree: Q = nCΔT. For gases, there are two values: Cᵥ (at constant volume) and Cₚ (at constant pressure). For ideal gases: Cₚ − Cᵥ = R.
Water has an unusually high specific heat capacity (4186 J/kg·K), which is why oceans moderate coastal climates and why water is used as a coolant.
10.7 Calorimetry
Calorimetry is the science of measuring heat. The principle of calorimetry is: heat lost by hot body = heat gained by cold body (at thermal equilibrium).
When mixing substances in different states (solid + liquid), remember: heat to raise temperature + latent heat for phase change = total heat exchanged. Always track which direction heat flows!
10.8 Change of State
Matter can exist in three states: solid, liquid, and gas. Changes between states require latent heat — heat absorbed or released without temperature change.
| Process | Latent Heat | Value (Water) | Effect |
|---|---|---|---|
| Fusion (melting) | Lf | 3.42 × 10⁵ J/kg | Solid → Liquid (absorbs heat) |
| Vaporization | Lv | 2.26 × 10⁶ J/kg | Liquid → Gas (absorbs heat) |
| Sublimation | Ls | — | Solid → Gas (absorbs heat) |
The Moon has no atmosphere because its low gravity can't hold gases. Day temperature ~120°C, night ~−180°C — huge range because no air to transfer heat or insulate.
10.9 Heat Transfer
Heat can be transferred by three mechanisms: conduction, convection, and radiation.
Conduction
Heat transfer through direct molecular contact without bulk movement. Good conductors: metals. Poor conductors (insulators): wood, plastic, air.
Convection
Heat transfer by bulk movement of fluid molecules. Hot fluid rises, cold fluid sinks — creating convection currents.
- Sea breeze (day): Land heats faster → air rises → sea air moves in
- Land breeze (night): Sea retains heat → air rises → land air moves in
- Room heater: Heated air rises, cool air sinks, creating circulation
Radiation
Heat transfer by electromagnetic waves (mainly infrared). Requires no medium — this is how the Sun heats Earth through vacuum.
Greenhouse gases (CO₂, CH₄) absorb and re-emit infrared radiation, trapping heat in the atmosphere. This is natural and keeps Earth habitable, but excess CO₂ enhances the effect, causing global warming.
10.10 Newton's Law of Cooling
The rate of heat loss of a body is proportional to the temperature difference between the body and its surroundings:
This law explains why hot tea cools faster initially (when it's much hotter than room temperature) and then cools more slowly as it approaches room temperature.
Hot Beverages
Adding cold milk cools tea faster than waiting because it increases the temperature difference initially.
Building Insulation
Insulation slows heat loss, keeping buildings warm in winter and cool in summer.
Thermos Flask
Vacuum insulation minimizes all three heat transfer modes to keep drinks hot/cold for hours.
Cooling Baked Goods
Hot cookies cool quickly at first, then slowly approach room temperature — Newton's law in action.