Question

Three rods made of the same material and the same cross-sectional areas have been joined as shown in the figure. Each rod is of the same length. The temperature of the junction is

• A. \(60^{\circ }\text{C}\)
• B. \(45^{\circ }\text{C}\)
• C. \(30^{\circ }\text{C}\)
• D. \(20^{\circ }\text{C}\)

Hint:

At steady state the heat entering the junction through the two hot rods equals the heat leaving through the cold rod.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Identical rods have equal thermal resistance, so heat current is proportional to the temperature difference.
Let the junction be at \(T\).

Step 2: Steady state
Heat in through two rods = heat out through one rod:
\(2(90-T)=T-0\)

Step 3: Solve
\(180-2T=T\)
\(3T=180\)
\(T=60^{\circ}\text{C}\)

Final Answer:
The junction temperature is 60 degrees Celsius. \[ \boxed{\text{(A) }60^{\circ}\text{C}} \]