Part of JME-10 — Thermal Properties: Expansion, Calorimetry & Heat Transfer

Thermal Radiation

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All bodies above 0 K emit thermal radiation (electromagnetic waves). Stefan-Boltzmann law: P=eσAT4P = e\sigma AT^4 for a body of emissivity ee (0 to 1), area AA, at temperature TT. The constant σ=5.67×108\sigma = 5.67 \times 10^{-8} W m2^{-2} K4^{-4}. Net radiation in surroundings at TsT_s: Pnet=eσA(T4Ts4)P_{\text{net}} = e\sigma A(T^4 - T_s^4).

Wien's displacement law: λmaxT=2.898×103\lambda_{\max} T = 2.898 \times 10^{-3} m K — hotter objects emit at shorter wavelengths. The Sun (5800 K) peaks at 500 nm (visible); human body (310 K) peaks at 9.4 micrometers (infrared).

Kirchhoff's law: at thermal equilibrium, emissivity = absorptivity (e=ae = a). Good absorbers are good emitters. A blackbody (e=1e = 1) is the ideal case.

Key radiation scaling: PT4P \propto T^4 means small temperature increases cause large power changes. Doubling absolute temperature gives 16x radiation. Critical trap in JEE: always convert to Kelvin before using radiation formulas — 27 degrees C = 300 K, not 27 K.

Cooling rate of a sphere: dT/dt1/rdT/dt \propto 1/r — smaller bodies cool faster (higher surface-to-volume ratio).

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