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JEE Main 202522 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
22 January
Shift
Morning Shift
Subject
Physics
Chapter
Thermal Properties of Matter

JEE Main 2025 · 22 January · Morning Shift · Physics · Thermal Properties of Matter

Three conductors of same length having thermal conductivity k_1,...

Three conductors of same length having thermal conductivity k1,k2\mathrm{k}_1, \mathrm{k}_2 and k3\mathrm{k}_3 are connected as shown in figure. Three conductors of same length having thermal conductivity k_1, k_2 and k_3 are connected as shown in figure. Area of
Area of cross sections of 1st 1^{\text{st }} and 2nd 2^{\text{nd }} conductor are same and for 3rd 3^{\text{rd }} conductor it is double of the 1st 1^{\text{st }} conductor. The temperatures are given in the figure. In steady state condition, the value of θ\theta is _______ ∘C{ }^{\circ} \mathrm{C}. (Given : k1=60Js−1 m−1 K−1,k2=120Js−1 m−1 K−1,k3=135Js−1 m−1 K−1\mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_3=135 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1} )

Correct answer

0

Step-by-step solution

Three conductors of same length having thermal conductivity k_1, k_2 and k_3 are connected as shown in figure. Area of
R1=2 L K1 AR2=2 L K2 AR3=LK3 Aθ−100R1R2R1+R2+θ−0R3=0θ=40\begin{aligned} & \mathrm{R}_1=\frac{2 \mathrm{~L}}{\mathrm{~K}_1 \mathrm{~A}} \\ & \mathrm{R}_2=\frac{2 \mathrm{~L}}{\mathrm{~K}_2 \mathrm{~A}} \\ & \mathrm{R}_3=\frac{\mathrm{L}}{\mathrm{K}_3 \mathrm{~A}} \\ & \frac{\theta-100}{\frac{\mathrm{R}_1 \mathrm{R}_2}{\mathrm{R}_1+\mathrm{R}_2}}+\frac{\theta-0}{\mathrm{R}_3}=0 \\ & \theta=40\end{aligned}
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