Heat ConductionJEE Main

Thermal resistance — Ohm's law for heat — interactive Physics simulation for IIT-JEE.

Concept

Steady-state heat flow is Ohm's law with new names: temperature difference drives a heat current through a thermal resistance $R = L/kA$ . Series rods share the same current, so the junction settles where the two flows match; the worse conductor hogs most of the temperature drop.

Key formula

H = \frac{dQ}{dt} = \frac{kA\,\Delta T}{L} = \frac{\Delta T}{R}, \qquad R = \frac{L}{kA}

Derivation

Fourier's law: $H = -kA\,dT/dx$ . In steady state H is uniform along a rod, so T falls linearly.

Series junction: equate currents $\frac{k_1A(T_h - T_j)}{L} = \frac{k_2A(T_j - T_c)}{L}$ , giving $T_j = \frac{k_1T_h + k_2T_c}{k_1+k_2}$ (equal lengths). Exactly a resistor divider.

Scenarios to explore

Heat Conduction — Series rods, junction temperature & thermal resistance.

Real-world applications

Double-glazed windows: trapped air's huge R blocks heat.
Heat sinks & thermal paste in electronics.
Igloo walls & thermos flasks: engineering big R.

JEE exam tips

Map to circuits: ΔT ↔ V, H ↔ I, L/kA ↔ R — every circuit trick transfers.
Equal-length series pair: k_eff = 2k₁k₂/(k₁+k₂), the harmonic mean.
Parallel slabs (same faces): k_eff = (k₁A₁+k₂A₂)/(A₁+A₂), the weighted mean.

Common mistakes

Averaging the two ks — combine RESISTANCES, not conductivities.
Forgetting that in series the same H flows through both rods.
Parallel rods: add currents (1/R), not resistances.

Exam traps to avoid

The steeper temperature gradient sits inside the POORER conductor.
Junction temperature is closer to the end connected by the BETTER conductor.