Two rods of same length and cross-sectional area are joined in series. Thermal conductivity of the rods are in ratio of 2 : 1.The ends are maintained at temperatures θ A and θ B as shown with θ A

Question

Two rods of same length and cross-sectional area are joined in series. Thermal conductivity of the rods are in ratio of 2 : 1.The ends are maintained at temperatures $θ_{A}$ and $θ_{B}$ as shown with $θ_{A} > θ_{B}$ and sides are thermally insulated. Which of the following graph represents temperature gradient $(\frac{dT}{dx})$ against x in steady state.

TestHub · Accepted Answer

In steady state the heat current is the same in both rods, so the temperature gradient is inversely proportional to conductivity:

$\frac{d T}{d x} \propto \frac{1}{K}$

gradient is constant within each rod, half as steep in the 2K rod as in the K rod. Only graph D shows two constant levels with the 2K section having the smaller gradient. Answer D.

Physics - Heat & Thermo Question with Solution | TestHub

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