Thermal Physics • Molecular Motion
Anomalous expansion of water • Specific heat capacity & numericals • Thermometers • Temperature scales
Thermal Energy & Molecular Motion
Definition: Thermal energy is the total kinetic energy of particles (atoms/molecules) due to their random motion. Higher temperature → faster molecular motion → greater thermal energy.
Kinetic Molecular Theory
- Molecules in constant random motion.
- Temperature ~ average kinetic energy (KEavg = ½ mv² ∝ T).
- Absolute zero (0 K) = minimum possible molecular motion.
- Thermal expansion: increased motion → increased spacing.
🔁 Short Trick: “Hot molecules dance faster” → KE = 3/2 kT (per molecule).
Formula: ΔU = m c ΔT (change in internal energy for ideal gas).
Formula: ΔU = m c ΔT (change in internal energy for ideal gas).
Visual fact Brownian motion: visible evidence of molecular collisions.
📌 Terminology: Thermal equilibrium – no net heat flow; Diffusion – random mixing due to motion.
Anomalous Expansion of Water
Definition: Water does NOT expand uniformly on heating. Between 0°C and 4°C, water contracts (density increases); above 4°C it expands normally. Maximum density occurs at 4°C.
Why it matters?
- ❄️ Ice floats (density ~917 kg/m³, water ~1000 kg/m³ at 4°C).
- 🌊 Lakes freeze top-down → aquatic life survives winter.
- 🧊 Bursting pipes: water freezes → expands by ~9%.
🧠 Memory trick: “4°C is water’s magic density peak” – “4 = for life”.
Anomalous behaviour = hydrogen bonding & open hexagonal structure in ice.
Anomalous behaviour = hydrogen bonding & open hexagonal structure in ice.
Example numerical (density): Mass of water = 1000 g at 4°C occupies 1.000 L. At 0°C, density = 0.99987 g/cm³ → volume expands. Ideal for conceptual understanding.
Specific Heat Capacity (c) & Numericals
Definition: Amount of heat required to raise the temperature of 1 kg (or 1 g) of substance by 1°C (or 1 K). Formula: Q = m c ΔT where Q = heat energy (J), m = mass (kg or g), c = specific heat (J/kg°C), ΔT = change in temp.
Water has high specific heat = 4186 J/kg°C (1 cal/g°C) → acts as thermal buffer. Metals have low c (e.g., iron ~450 J/kg°C).
Solved numerical 1
🔥 How much heat is needed to raise temp of 2 kg of water from 20°C to 80°C? (c_water = 4186 J/kg°C)
Solution: ΔT = 60°C, Q = m c ΔT = 2 × 4186 × 60 = 502,320 J = 502.32 kJ.
Numerical 2 (Metal)
A 0.5 kg copper piece absorbs 4,500 J and temperature rises from 25°C to 45°C. Find specific heat of copper.
Solution: ΔT = 20°C, Q = m c ΔT → c = Q/(mΔT) = 4500/(0.5×20) = 4500/10 = 450 J/kg°C. ✅ (Matches copper)
Formula variations
- Heat lost = Heat gained (principle of calorimetry)
- c = Q/(m ΔT) , ΔT = Q/(m c)
Mnemonic: “Q = mcΔT → Queen Makes Cool Temperature”
Thermometers | Laboratory, Clinical, Digital
Laboratory thermometer
Range: -10°C to 110°C. Uses mercury or alcohol. No constriction. Used for experiments.
Clinical thermometer
Range: 35°C – 42°C (95°F – 108°F). Has kink/constriction to hold reading after removal. Mercury or galinstan.
Digital thermometer
Uses thermistor / RTD / infrared sensor. Fast, accurate, LCD display. No mercury.
Infrared Non-contact forehead thermometers.
✨ Trick: “Kink in clinical → keeps reading; No kink in lab → continuous response.”
| Type | Range | Special Feature |
|---|---|---|
| Laboratory | -10°C – 110°C | No constriction, partial immersion |
| Clinical | 35°C – 42°C | Constriction, sterilization required |
| Digital | -50°C – 300°C (varies) | Thermistor, fast response |
Temperature Scales: Celsius, Fahrenheit, Kelvin
Absolute scale: Kelvin (K) – no negative temperatures, 0 K = absolute zero (-273.15°C).
Conversion formulas
- °C to K: K = °C + 273.15
- K to °C: °C = K – 273.15
- °F to °C: °C = (°F – 32) × 5/9
- °C to °F: °F = (°C × 9/5) + 32
Mnemonics: “K = C + 273 (Keep Cold +273)”
“Fahrenheit Furious: subtract 32, multiply by 5/9”
“Fahrenheit Furious: subtract 32, multiply by 5/9”
📌 Example: Convert 100°F to °C.
(100 – 32) × 5/9 = 68 × 5/9 = 37.78°C ✅
Quick reference: triple point & absolute zero
Absolute zero 0 K = -273.15°C
Water freezes 0°C = 32°F = 273.15 K
Water boils 100°C = 212°F = 373.15 K
Interactive MCQs & Terminologies Q&A
Test yourself: Click on Show Answer after attempting.
Q1. Which temperature scale does NOT have negative values?
A) Celsius B) Fahrenheit C) Kelvin D) Rankine
A) Celsius B) Fahrenheit C) Kelvin D) Rankine
✅ Answer: C) Kelvin – absolute scale starts at 0 K.
Q2. At what temperature does water have maximum density?
A) 0°C B) 4°C C) 100°C D) -4°C
A) 0°C B) 4°C C) 100°C D) -4°C
✅ Answer: B) 4°C – anomalous expansion peak density.
Q3. The specific heat capacity of water is approx:
A) 4186 J/kg°C B) 1 J/g°C C) Both A & B D) 4200 kJ/kg°C
A) 4186 J/kg°C B) 1 J/g°C C) Both A & B D) 4200 kJ/kg°C
✅ Answer: C) Both A & B (since 1 cal/g°C = 4186 J/kg°C).
Q4. Which thermometer has a constriction (kink) to retain reading?
A) Laboratory B) Digital C) Clinical D) Pyrometer
A) Laboratory B) Digital C) Clinical D) Pyrometer
✅ Answer: C) Clinical thermometer – kink prevents mercury backflow.
Q5. If molecular motion stops completely, temperature is:
A) 0°C B) -273°C C) 0 K D) Both B & C
A) 0°C B) -273°C C) 0 K D) Both B & C
✅ Answer: D) Both B and C (Absolute zero = -273.15°C = 0 K).
Q&A with key terminologies (click to reveal)
❓ What is “specific heat capacity” in simple words?
Term: Specific heat capacity (c) = heat needed per unit mass per unit temperature change. High c → resists temperature changes (water acts as thermal regulator).
❓ Explain “Anomalous expansion of water” and its significance.
Term: Anomalous expansion: water contracts from 0°C to 4°C, expands above 4°C. Significance: marine life survives winter as ice floats, water bodies freeze from top down.
❓ Relation between thermal energy and molecular motion? State formula.
Formula: Average kinetic energy = (3/2)kT, where k = Boltzmann constant. Higher temperature → faster RMS speed → vrms = √(3RT/M).
❓ How does a digital thermometer work?
Working: Uses thermistor (resistance changes with temperature) → converts to voltage → microcontroller displays temperature on LCD. Instant readout.
❓ A 100 g iron piece at 200°C is dropped into 200 g water at 20°C (c_iron = 450 J/kg°C, c_water = 4186 J/kg°C). Find final equilibrium temperature.
Solution: Heat lost = heat gained: m₁c₁(T₁ – T_f) = m₂c₂(T_f – T₂).
0.1 × 450 × (200 – T_f) = 0.2 × 4186 × (T_f – 20) → 45(200 – T_f) = 837.2(T_f – 20) → 9000 – 45T_f = 837.2T_f – 16744 → 9000+16744 = 837.2T_f+45T_f → 25744 = 882.2 T_f → T_f ≈ 29.18°C. ✅
0.1 × 450 × (200 – T_f) = 0.2 × 4186 × (T_f – 20) → 45(200 – T_f) = 837.2(T_f – 20) → 9000 – 45T_f = 837.2T_f – 16744 → 9000+16744 = 837.2T_f+45T_f → 25744 = 882.2 T_f → T_f ≈ 29.18°C. ✅
Extra Detailing: Tables & Terminologies
Specific heat values (J/kg°C)
- Water: 4186
- Ice: 2100
- Aluminium: 900
- Copper: 385
- Lead: 130
Thermal expansion formulas
- Linear: ΔL = α L₀ ΔT
- Volumetric: ΔV = β V₀ ΔT (β ≈ 3α for solids)
- Water volumetric anomaly: β negative 0–4°C
Memory: “α αlpha expansion linear, β βeta bulk”
Quick facts:
• Molecular motion increases with T → more collisions → pressure increase (Gay-Lussac)
• Latent heat: hidden heat during phase change (no ΔT).
• Calorimetry principle: heat gain = heat loss in isolated system.
• Molecular motion increases with T → more collisions → pressure increase (Gay-Lussac)
• Latent heat: hidden heat during phase change (no ΔT).
• Calorimetry principle: heat gain = heat loss in isolated system.
Important terminologies glossary
Thermal equilibrium – when two bodies reach same temperature.
Heat capacity – C = mc (J/°C).
Calorimeter – device to measure heat exchange.
Triple point of water – 0.01°C, 611 Pa – unique T where ice, water, vapor coexist.
Thermometric property – physical property changing with T (length, resistance, pressure).