Question

Three identical thermal conductors are connected as shown in figure. Considering no heat loss due to radiation, temperature at the junction will be

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• A. $40^{\circ}C$
• B. $60^{\circ}C$
• C. $50^{\circ}C$
• D. $35^{\circ}C$

Hint:

Three identical thermal conductors are connected as shown in figure. Considering no heat loss due to radiation, temperature at the junction will be \includegraphics[width=0.5\linewidth]3phy.png \labelfig:placeholder

Answer 1

The Correct Option is C

To find the temperature at the junction of three identical thermal conductors, we apply the principle of thermal equilibrium. The conductors are connected at a junction, and the temperatures at their free ends are given. Let's denote the temperatures as follows:

• \(T_1 = 20^{\circ}C\)
• \(T_2 = 60^{\circ}C\)
• \(T_3 = 70^{\circ}C\)

Assuming the conductors are identical, the heat conduction in each will satisfy the condition of being proportional to the temperature difference.

For thermal equilibrium, the sum of heat flow to the junction must equal the sum of heat flow out, which can be mathematically expressed as:

\(K(T_1 - T) + K(T_2 - T) + K(T_3 - T) = 0\)

Simplifying, we have:

\(T_1 + T_2 + T_3 - 3T = 0\)

Solving for \(T\):

\(T = \frac{T_1 + T_2 + T_3}{3}\)

Substitute the given temperatures:

\(T = \frac{20 + 60 + 70}{3} = \frac{150}{3} = 50^{\circ}C\)

The temperature at the junction will thus be 50°C.