Question

Three identical rods $AB,CDandPQ$ are joined as shown. $P$ and $Q$ are mid points of $AB$ and $CD$ respectively. Ends $A,B,C$ and $D$ are maintained at $0^{\circ }C,{100}^{\circ }C,{30}^{\circ }C$ and ${60}^{\circ }C$ respectively. The direction of heat flow in $PQ$ is :

• A. from $P$ to $Q$
• B. from $Q$ to $P$
• C. heat does not flow in $PQ$
• D. data not sufficient

Answer 1

Answer: (A)

from $P$ to $Q$

Both the rods AB and CD are in steady state.
i.e. the temperature gradient is a constant and the temperature drops linearly with distance.
Temperature at midpoint of AB = $\frac{T_A+T_B}{2}={50}^{\circ }C=T_P$
Temperature at midpoint of CD = $\frac{T_C+T_D}{2}={45}^{\circ }C=T_Q$
Since temperature at P is more than that at Q, heat flows from P to Q.