Thermal Properties of Matter
'Heat is a form of energy.' — James Prescott Joule
1. Chapter Overview
This chapter explores how MATTER behaves when HEAT is added or removed. Topics include THERMAL EXPANSION (solids, liquids, and gases), CALORIMETRY (heat measurement), CHANGE OF STATE (melting, boiling, latent heat), and HEAT TRANSFER mechanisms — CONDUCTION, CONVECTION, and RADIATION. These concepts bridge macroscopic observations with microscopic molecular motion.
2. Temperature and Heat
- Temperature: Measure of the AVERAGE kinetic energy of molecules (INTENSIVE property)
- Heat: Energy transferred BETWEEN systems due to temperature difference (EXTENSIVE property)
- Thermal Equilibrium: Two systems at the SAME temperature (Zeroth Law of Thermodynamics)
Temperature Scales
| Scale | Lower Fixed Point | Upper Fixed Point | Formula |
|---|---|---|---|
| Celsius (°C) | 0°C (ice point) | 100°C (steam point) | C = K — 273.15 |
| Fahrenheit (°F) | 32°F | 212°F | °F = (9/5)°C + 32 |
| Kelvin (K) | 273.15 K | 373.15 K | K = °C + 273.15 |
3. Thermal Expansion
Linear Expansion (Solids)
- ΔL = αL₀ΔT (α = coefficient of linear expansion)
- α: per °C or per K
Area (Superficial) Expansion
- ΔA = βA₀ΔT (β = 2α for isotropic materials)
Volume Expansion
- ΔV = γV₀ΔT (γ = 3α for isotropic materials)
Anomalous Expansion of Water
- Water has MINIMUM volume (maximum density) at 4°C
- Between 0°C and 4°C, water EXPANDS on cooling (contracts on heating)
- This is WHY ice floats and ponds freeze from the top down
Thermal Expansion of Liquids
- Apparent expansion (observed in container): γ_app = γ_real — γ_container
- Real expansion: γ_real = (1/V)(ΔV/ΔT)
Worked Problem
Q: A steel rail of length 20 m at 20°C. Find expansion at 45°C. (α = 1.2×10⁻⁵ /°C) A: ΔL = αL₀ΔT = 1.2×10⁻⁵ × 20 × (45 — 20) = 1.2×10⁻⁵ × 20 × 25 = 6×10⁻³ m = 6 mm.
4. Calorimetry
- Heat Capacity C = Q/ΔT (SI: J/K)
- Specific Heat Capacity c = Q/(mΔT) (SI: J/kg·K)
- Molar Specific Heat C = Q/(nΔT) (SI: J/mol·K)
Principle of Calorimetry
- Heat LOST by hot body = Heat GAINED by cold body
- m₁c₁(T₁ — T) = m₂c₂(T — T₂) (for two-body system)
- Assumes NO heat loss to surroundings
Worked Problem
Q: 200 g of water at 80°C is mixed with 100 g of water at 30°C. Find final temperature. A: 200×c×(80 — T) = 100×c×(T — 30) → 16000 — 200T = 100T — 3000 → 19000 = 300T → T = 63.3°C.
5. Change of State
Latent Heat
- Latent Heat of Fusion (L_f): Heat required to change 1 kg from solid to liquid at melting point
- Ice: L_f = 3.36×10⁵ J/kg
- Latent Heat of Vaporisation (L_v): Heat required to change 1 kg from liquid to vapour at boiling point
- Water: L_v = 22.6×10⁵ J/kg
Heating Curve of Water
- 0°C to 0°C (ice melting): Q = mL_f (temperature CONSTANT during phase change)
- 0°C to 100°C (water heating): Q = mcΔT
- 100°C to 100°C (water boiling): Q = mL_v (temperature CONSTANT)
Triple Point
- The UNIQUE temperature and pressure where all three phases (solid, liquid, vapour) coexist in equilibrium
Worked Problem
Q: How much heat is needed to convert 100 g of ice at -10°C to steam at 100°C? (c_ice = 2100 J/kg·K, L_f = 3.36×10⁵ J/kg, L_v = 22.6×10⁵ J/kg) A: Q₁ = mcΔT_ice = 0.1×2100×10 = 2100 J. Q₂ = mL_f = 0.1×3.36×10⁵ = 33600 J. Q₃ = mcΔT_water = 0.1×4200×100 = 42000 J. Q₄ = mL_v = 0.1×22.6×10⁵ = 226000 J. Total = 303700 J.
6. Heat Transfer
Conduction
- Fourier's Law: Q/t = kA(ΔT/d) (k = thermal conductivity, W/m·K)
- Thermal Resistance: R = d/kA
- Good conductors: Metals (k ≈ 200-400 W/m·K)
- Insulators: Wood, air, glass wool (k ≈ 0.01-0.1 W/m·K)
Convection
- Heat transfer by the ACTUAL MOVEMENT of heated material
- Natural convection: Warm fluid rises (density decrease)
- Forced convection: Fan or pump circulates fluid
- Examples: Sea breeze, land breeze, household heating
Radiation
- Heat transfer by ELECTROMAGNETIC WAVES (does NOT require medium)
- Stefan-Boltzmann Law: P = εσAT⁴ (σ = 5.67×10⁻⁸ W/m²·K⁴)
- Wien's Displacement Law: λ_m T = b (b = 2.9×10⁻³ m·K)
- Higher temperature → shorter peak wavelength
- Sun (~5800 K) emits mostly visible; Earth (~300 K) emits infrared
Newton's Law of Cooling
- Rate of cooling ∝ Temperature difference with surroundings
- dT/dt = -k(T — T₀)
- Approximate for moderate temperature differences
7. Common Mistakes
- Temperature and heat are NOT the same: Heat is energy transfer; temperature measures average KE
- Phase changes occur at CONSTANT temperature: Adding heat during melting/boiling does NOT raise temperature
- Water expansion anomaly: Water expands when cooled from 4°C to 0°C (unlike most substances)
- Radiation does NOT require a medium: The Sun's heat reaches Earth through the vacuum of space
- Newton's law of cooling is approximate: It's accurate only when the temperature difference is small
8. CBSE Exam Focus
- Thermal expansion numericals — gaps in rails, bimetallic strips
- Calorimetry — mixture problems (3/5-mark)
- Latent heat — phase change calculations (5-mark)
- Heat conduction — thermal resistance and composite walls
- Stefan-Boltzmann law and Wien's displacement law
- Newton's law of cooling — numericals
9. Key Formulas
- ΔL = αL₀ΔT, ΔA = βA₀ΔT, ΔV = γV₀ΔT (β = 2α, γ = 3α)
- Q = mcΔT (sensible heat)
- Q = mL (latent heat)
- Q/t = kA(ΔT/d) (conduction)
- P = εσAT⁴ (radiation), σ = 5.67×10⁻⁸ W/m²·K⁴
- λ_m T = constant (2.9×10⁻³ m·K)
- dT/dt = -k(T — T₀) (Newton's cooling)
10. Self-Test (5+ Q&A)
Q1: A 100 g copper block (c = 390 J/kg·K) at 200°C is placed in 200 g water at 20°C. Find final temperature. A: Heat lost = Heat gained: 0.1×390×(200 — T) = 0.2×4200×(T — 20) → 39(200 — T) = 840(T — 20) → 7800 — 39T = 840T — 16800 → 24600 = 879T → T = 28°C.
Q2: Why does a brass disc pass through a brass ring when both are heated equally? A: Both expand equally (same α). The hole expands as if it were made of the same material, so the disc still fits.
Q3: At what temperature is the Celsius reading equal to Fahrenheit? A: C = (9/5)C + 32 → -40°C = -40°F.
Q4: Calculate the cooling rate of a body at 60°C in surroundings at 30°C if it cools from 50°C to 40°C in 5 minutes. A: Newton's law: Rate = -kΔT_avg. This requires experimental data or the constant k.
Q5: Why is the bottom of a lake warmer than the top in winter? A: Anomalous expansion of water: Water is densest at 4°C. In winter, surface water cools and sinks until the whole lake reaches 4°C. Further cooling makes surface water less dense (0-4°C), so it stays on top and freezes.
11. Conclusion
Thermal properties connect the MICROSCOPIC (molecular kinetic energy) to the MACROSCOPIC (expansion, heat transfer). Understanding thermal expansion is crucial in engineering (expansion joints, thermostats). Calorimetry is the practical measurement of heat. Phase changes involve LARGE amounts of energy at constant temperature. Heat transfer mechanisms explain everything from cooking to climate. This chapter forms the BRIDGE to thermodynamics.
