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Temperature of the junction of conductors joined in series (steady state)

This type of question, asked 5 times: 2021 Paper 25, 27 Jul 2022, 13 Apr 2023, 7 Apr 2025, 22 Jan 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 25

    2
    The temperature θ\theta at the junction of two insulating sheets, having thermal resistances R1R_{1} and R2R_{2} as well as top and bottom temperatures θ1\theta_{1} and θ2\theta_{2} (as shown in figure) is given by:

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  2. Question 2

    27 Jul 2022

    7
    If K1K_{1} and K2K_{2} are the thermal conductivities L1L_{1} and L2L_{2} are the lengths and A1A_{1} and A2A_{2} are the cross sectional areas of steel and copper rods respectively such that K2K1=9,A1A2=2,L1L2=2\frac{K_{2}}{K_{1}}= 9,\frac{A_{1}}{A_{2}}= 2,\frac{L_{1}}{L_{2}}= 2. Then, for the arrangement as shown in the figure. The value of temperature TT of the steel - copper junction in the steady state will be:

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  3. Question 3

    13 Apr 2023

    119
    Two plates AA and BB have thermal conductivities 84Wm−1 K−184Wm^{- 1}{\text{ }K}^{- 1} and 126Wm−1 K−1126Wm^{- 1}{\text{ }K}^{- 1} respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at 100 ∘C100\ ^{\circ}C and 0 ∘C0\ ^{\circ}C respectively, then the temperature of the surface of contact in steady state is_____  ∘C\ ^{\circ}C.
  4. Question 4

    7 Apr 2025

    98
    Two cylindrical rods AA and BB made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are : LALB=12,rArB=2\frac{L_{A}}{L_{B}} = \frac{1}{2},\frac{r_{A}}{r_{B}} = 2 and KAKB=12\frac{K_{A}}{K_{B}} = \frac{1}{2}. The free ends of rods A and B are maintained at 400 K,200 K400\text{ }K,200\text{ }K, respectively. The temperature of rods interface is ____\_\_\_\_ K, when equilibrium is established.
  5. Question 5

    22 Jan 2026 S1

    13
    Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points AA and FF are maintained at 100∘C100^{\circ}C and 40∘C40^{\circ}C respectively. Given the thermal conductivity of rod x is three times of that of rod y , the temperature at junction points BB and EE are (close to) :

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