Two conductors A and B each of cross section area 5 cm2 are connected in series. Variation of temperature (in ºC) along the length (in cm) is as shown in the figure. If thermal conductivity of A is 200 J/m-sec-ºC. The thermal conductivity of B is K × 50\sqrt{3} J/m-sec-ºC. Find the value of K.

Engineering

Physics

Conduction of Heat

Thermal Expansion

Question

Two conductors A and B each of cross section area 5 cm² are connected in series. Variation of temperature (in ºC) along the length (in cm) is as shown in the figure. If thermal conductivity of A is 200 J/m-sec-ºC. The thermal conductivity of B is K × 50 $\sqrt{3}$ J/m-sec-ºC. Find the value of K.

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$\frac{ΔQ}{Δt} = K_{A} A \frac{dT}{dx}$
$\frac{dT}{dx}$ in conductor A = slpoe of graph = $\sqrt{3}$
Since both conductors are connected in series, same heat current will flow in A and B.
$K_{B} = \frac{ΔQ}{Δt} \times \frac{1}{A \frac{dT}{dn}} = \frac{Δθ}{Δt} \times \frac{1}{Atan 45^{\circ}} = 200 \sqrt{3} J / m - \sec^{\circ} C$