See Our New JEE Book on Amazon

**Problem:**
Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of junction of the three rods will be?
(IIT JEE 2001)

- 45°C
- 60°C
- 30°C
- 20°C

**Answer:** The answer is (B) i.e., temperture of junction of the three rods is 60°C.

**Solution:**
Let T be the temperature of the junction. The rate of heat flow to the junction is
\begin{align}
\frac{\mathrm{d}Q_\text{in}}{\mathrm{d}t}&=\kappa A \frac{(90-T)}{l}+\kappa A \frac{(90-T)}{l}\nonumber\\
&=2\kappa A \frac{(90-T)}{l},
\end{align}
and the rate of heat flow out of the junction is
\begin{align}
\frac{\mathrm{d}Q_\text{out}}{\mathrm{d}t}=\kappa A \frac{(T-0)}{l}=\frac{\kappa AT}{l}.
\end{align}
In steady state, the rate of inflow of heat at the junction is equal to the rate of outflow of heat i.e.,
\begin{align}
\frac{\mathrm{d}Q_\text{in}}{\mathrm{d}t}=\frac{\mathrm{d}Q_\text{out}}{\mathrm{d}t}.
\end{align}
Solve above equations to get temperature of junction of the three rods T = 60°C.

- Heat Conduction
- The end Q and R of two thin wires, PQ and RS, are soldered (IIT JEE 2016)
- Two blocks connected in series and parallel ( IIT JEE 2013)
- Two rods connected in series and parallel (IIT JEE 2014)
- Two conducting cylinders of equal length but different radii connected in series (IIT JEE 2018)
- Three rods forms an isosceles triangle. Temperature at the vertex? (IIT JEE 1995)
- Effective thermal conductivity of two concentric cylinders (IIT JEE 1988)
- Evaporation of water and melting of ice kepts at two ends of a metal rod AB of length 10x (IIT JEE 2009)
- MCQ on a composite block is made of slabs A, B, C, D, and E (IIT JEE 2011)
- A point source of heat of power P kept at the centre of a spherical shell (IIT JEE 1991)
- A double pane window used for insulating a room thermally from outside (IIT JEE 1997)
- An electric heater is used in a room of total wall area 137 m
^{2}( IIT JEE 1986)