Day Before Exam Protocol: Don't study new material. Use this page only. Go through flashcards (2 passes), formula dump (1 pass), and rapid-fire Q&A (1 pass). Sleep 8 hours. Confidence > Last-minute cramming.
✅ Topic Checklist
Mark What You've Mastered
Temperature scales
Linear expansion (α)
Area expansion (β)
Volume expansion (γ)
α:β:γ = 1:2:3
Thermal stress
Anomalous expansion
Real vs Apparent expansion
Specific heat (Q=mcΔT)
Latent heat (Q=mL)
Calorimetry + phase check
Heating curve
Fourier's Law (conduction)
Thermal resistance
Series/parallel slabs
Newton's Law of Cooling
Stefan-Boltzmann Law
Wien's Displacement Law
Kirchhoff's Law
Blackbody concept
🃏 Flashcards
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📐 Formula Dump
All Formulas at a Glance
The complete formula set — organized for last-minute revision.
Temperature Conversion
K = °C + 273.15; F = (9/5)C + 32
Linear Expansion
ΔL = αL₀ΔT; L = L₀(1+αΔT)
Area Expansion
ΔA = βA₀ΔT; β = 2α
Volume Expansion
ΔV = γV₀ΔT; γ = 3α
Relation α:β:γ
α : β : γ = 1 : 2 : 3
Thermal Stress
Stress = Y·α·ΔT; Force = Y·A·α·ΔT
Real vs Apparent
γ_real = γ_apparent + γ_vessel
Heat (No Phase Change)
Q = m·c·ΔT
Latent Heat
Q = m·L (T is constant!)
Calorimetry
Heat lost = Heat gained
Fourier's Conduction
H = KA(T₁-T₂)/L
Thermal Resistance
R = L/(KA); Series: R_total = ΣR
Newton's Cooling
dT/dt = -k(T-T₀)
Newton's Cooling Solution
T(t) = T₀ + (T_i-T₀)e^(-kt)
Stefan-Boltzmann Law
P = eσAT⁴ (T in Kelvin!)
Net Radiation Power
P_net = eσA(T⁴ - T₀⁴)
Wien's Displacement Law
λ_max · T = 2.898×10⁻³ m·K
Kirchhoff's Law
emissivity (e) = absorptivity (a)
📋 Chapter at a Glance
Complete Summary Table
| Concept | Formula | Key Point | Exam Note |
|---|---|---|---|
| Temp. Conversion | K = °C + 273.15 | K is always used in radiation formulas | ⚠️ Never use °C in Stefan/Wien |
| Linear Expansion | ΔL = αL₀ΔT | α ≈ 10⁻⁵ K⁻¹ for metals | Hole EXPANDS (same β) |
| Volume Expansion | ΔV = γV₀ΔT; γ=3α | γ = 3α for isotropic solids | Anisotropic: γ = α₁+α₂+α₃ |
| Thermal Stress | Stress = YαΔT | Uses Young's Modulus | Compressive when heating |
| Anomalous Expansion | — | Water contracts 0→4°C; max density at 4°C | Why fish survive in winter |
| Specific Heat | Q = mcΔT | Water: 4186 J/kg·K (highest) | NOT for phase change |
| Latent Heat | Q = mL | L_fusion(ice) = 3.34×10⁵ J/kg | T = const during phase change |
| Conduction | H = KA(T₁-T₂)/L | R_th = L/KA (like electrical R) | Series: R_total = ΣR; Parallel: ΣKA |
| Newton's Cooling | dT/dt = -k(T-T₀) | Valid for small ΔT only | Graph: exponential decay to T₀ |
| Stefan-Boltzmann | P = eσT⁴ | σ = 5.67×10⁻⁸ W/m²K⁴ | P∝T⁴; double T → 16× power |
| Wien's Law | λ_max·T = 2.898×10⁻³ | Higher T → shorter λ | Sun (5800K) → 500nm (yellow) |
| Kirchhoff's Law | e = a | Good absorbers = good emitters | At thermal equilibrium |
🧠 Memory Tricks
Never Forget These Again
🔢 α:β:γ = 1:2:3
Think: "1D, 2D, 3D" → linear, area, volume. Each dimension multiplies α by another dimension. 1D=α, 2D=2α, 3D=3α.
One, Two, Three → Line, Area, Volume
🌡️ Kelvin = Celsius + 273
Think of 273 as the "absolute zero buffer." 0°C is not truly zero temperature — there's still 273 degrees of thermal energy. Absolute zero (0 K) means truly no thermal energy.
0°C = 273 K (not zero!)
💎 Stefan's Law — T⁴ Power
Double the temperature → 16× the radiation (2⁴ = 16). Triple it → 81× (3⁴ = 81). This non-linear growth is why stars are so luminous — small T increase = huge power jump.
2T → 16P; 3T → 81P (T⁴!)
🌊 Anomalous Expansion 0→4°C
Water is the exception. Think: ICE forms a lattice structure that is LESS DENSE than liquid water. As ice melts 0→4°C, this open lattice collapses → water contracts → denser. Above 4°C, normal expansion wins.
ICE lattice = sparse; breaking it = denser water
⚡ Thermal = Electrical Analogy
R_thermal = L/KA mimics R_electrical = ρL/A. Heat current (H) = ΔT/R_th mimics I = V/R. Series: R_total = R₁+R₂. Parallel: 1/R = 1/R₁+1/R₂. This analogy solves ALL multi-slab problems.
H↔I, ΔT↔V, R_th↔R, K↔1/ρ
🌊 Newton's Cooling
Rate of cooling ∝ excess temperature. As body approaches surrounding temp, rate DECREASES exponentially. Like a ball decelerating — it never fully stops but gets closer and closer.
dT/dt ↓ as (T-T₀) ↓ → Never exactly T₀
⚡ Rapid Fire
Tap to Reveal Answers
Test yourself in 2 minutes. For last-day revision.
Q1. What is the SI unit of temperature?
Kelvin (K)
Q2. State the relation between α, β, and γ for isotropic solids.
α : β : γ = 1 : 2 : 3 → β = 2α, γ = 3α
Q3. At what temperature does water have maximum density?
4°C (anomalous expansion of water)
Q4. Write Fourier's Law of heat conduction.
H = KA(T₁−T₂)/L, where K = thermal conductivity
Q5. State Kirchhoff's Law of radiation.
Emissivity = Absorptivity (e = a) at thermal equilibrium. Good absorbers are good emitters.
Q6. What is the value of Stefan's constant σ?
σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
Q7. If a body's temperature doubles, how does its rate of radiation change?
Increases 16× (P ∝ T⁴; 2⁴ = 16)
Q8. Does a hole in a metal plate expand or contract on heating?
EXPANDS — all dimensions increase with thermal expansion, including holes.
Q9. State Newton's Law of Cooling (mathematical form).
dT/dt = −k(T − T₀), valid for small temperature excess over surroundings.
Q10. What is the thermal stress in a constrained rod heated by ΔT?
Thermal Stress = Y × α × ΔT (Y = Young's Modulus)
Q11. What is the latent heat of fusion of water?
L_f = 3.34 × 10⁵ J/kg = 80 cal/g
Q12. What does Wien's Displacement Law state?
λ_max × T = 2.898×10⁻³ m·K. Higher temp = smaller peak wavelength (bluer light).
🎯 Final Exam Day Tip
You've completed all 11 modules. The difference between good preparation and great preparation is: knowing WHY, not just WHAT. In the exam, when you see an unfamiliar problem — don't panic. Break it into: What type of thermal process? What conservation law applies? What formula subset? These three questions solve 90% of problems.
You've got this. Go get that rank. 🚀
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