Heat Transfer — Quick & Fun Notes 😎🔥

Heat moves whenever there’s a temperature difference. It travels in three distinct ways:

  • Conduction 🧱
  • Convection 🌬️
  • Radiation ☀️

1 · Conduction 🧱➡️🧊

Conduction is particle-to-particle energy transfer inside a solid, or between solids in contact. Picture one end of a metal rod in a flame; the other end soon feels hot because vibrations/energy march along the lattice. Gases conduct poorly, liquids sit in between solids and gases.

The steady-state heat current is

\[ H \;=\; \frac{K\,A\bigl(T_C – T_D\bigr)}{L} \]

where

  • K = thermal conductivity (material property)
  • A = cross-sectional area
  • L = length between the hot end at \(T_C\) and the cold end at \(T_D\)

Higher K means better heat conductor. 🏎️:contentReference[oaicite:0]{index=0}

Typical K values (W m−1 K−1):

  • Silver 406, Copper 385, Aluminium 205
  • Steel 50, Glass 0.8, Wood 0.12
  • Air 0.024 (notice how tiny!)

That’s why saucepans get copper bottoms (great spread of heat) and fluffy quilts trap pockets of air (great insulators).:contentReference[oaicite:1]{index=1}

Cool example: A steel rod (15 cm) welded to a copper rod (10 cm) gives a junction temperature of about 44 °C when one end sits in a 300 °C furnace and the other in ice water.:contentReference[oaicite:2]{index=2}

2 · Convection 🌬️

Convection needs a fluid. Warm parts expand, become lighter, and rise; cooler parts sink and the cycle keeps moving heat around.

  • Natural convection – driven purely by buoyancy. Classic daytime sea-breeze: land heats up faster than sea, warm air over land rises, cool sea air rushes in. At night the cycle flips.:contentReference[oaicite:3]{index=3}
  • Forced convection – we shove the fluid along with a pump or fan: home heaters, car radiators, even your bloodstream (your heart is the pump!).:contentReference[oaicite:4]{index=4}

🌍 Trade winds are another giant-scale convection story, tweaked by Earth’s rotation.

3 · Radiation ☀️

Radiation zips through vacuum as electromagnetic waves at light-speed (3 × 108 m/s). No material medium needed — that’s how sunlight warms us across space.:contentReference[oaicite:5]{index=5}

3.1 Stefan–Boltzmann law 🥵➡️📤

A perfect emitter (a “blackbody”) radiates energy at

\[ H \;=\; \sigma\,A\,T^{4} \]

with \(\sigma = 5.67 \times 10^{-8}\,\text{W m}^{-2}\text{K}^{-4}\). Real objects use an emissivity \(e\) (0 ≤ e ≤ 1):

\[ H \;=\; e\,\sigma\,A\bigl(T^{4} – T_s^{4}\bigr) \]

So a person (skin emissivity ≈ 0.97, area ≈ 1.9 m²) at skin temperature 28 °C in a 22 °C room loses about 66 W by radiation alone — that’s half your resting power output!:contentReference[oaicite:6]{index=6}

3.2 Colour & everyday hacks 🎨

  • Black surfaces absorb and emit best; shiny silvers reflect. That’s why we wear light clothes in summer and dark ones in winter, and why a thermos has silvered walls to bounce radiation back inside.:contentReference[oaicite:7]{index=7}

3.3 Blackbody spectrum & Wien’s law 🌈

Thermal radiation contains all wavelengths but peaks at one that shifts with temperature:

\[ \lambda_m\,T \;=\; 2.9 \times 10^{-3}\,\text{m·K} \]

Heat a metal: dull red → yellow → white as the peak slides to shorter wavelengths.:contentReference[oaicite:8]{index=8}

Bonus Worked Problem 💪

Turning 3 kg of ice at –12 °C into steam at 100 °C needs four steps (warm ice, melt, warm water, vaporize). Add all four energy chunks and you get about \(9.1\times10^{6}\) J.:contentReference[oaicite:9]{index=9}

High-Yield NEET Nuggets 🏆

  1. Conduction formula \(H = \dfrac{K\,A\,(T_C – T_D)}{L}\) — expect questions on rod junction temperatures and composite bars.
  2. Stefan–Boltzmann net loss \(H = e\sigma A (T^{4} – T_s^{4})\) — favourite for “power radiated” calculations.
  3. Wien’s displacement law \(\lambda_m T = 2.9\times10^{-3}\,\text{m·K}\) — often used to estimate star or filament temperatures.
  4. Order of thermal conductivities (Silver > Copper > Aluminium ≫ Glass > Air) — useful for reasoning, no calculator needed.
  5. Modes comparison — be clear which mechanism works in vacuum (only radiation) and which need matter (conduction, convection).

Keep practising with cheerful curiosity, and heat-transfer questions will feel like a warm breeze! 🌬️💡