Question

Two identical square rods of metal are welded end to end as shown in the figure $\left(\right.1\left.\right)$ , $20 \, cal$ of heat flows through it in $4 \, min$ . If the rods are welded as shown in the figure $\left(\right.2\left.\right)$ , the same amount of heat will flow through the rods in

• A. $1 \, min$
• B. $2min$
• C. $4min$
• D. $16min$

Answer 1

Answer: (A)

Figure (1) $ \rightarrow $ series combination
Figure (2) $ \rightarrow $ parallel combination
Thermal resistance for each block to be $\textit{R}$
Then
Thermal resistance for the case I $\textit{R}_{1}=2\textit{R}$
Thermal resistance for the case II $\textit{R}_{2}=\textit{R}\text{/2}$
Thermal resistance for case II
$\text{I}_{1} = \frac{\Delta \text{T}}{\text{R}_{1}}$ $\text{I}_{2} = \frac{\Delta \text{T}}{\text{R}_{2}}$
$\Rightarrow 4 \text{I}_{1} = \text{I}_{2}$
$4\frac{\Delta Q_{1}}{\Delta \text{t}_{1}}=\frac{\Delta Q_{2}}{\Delta \text{t}_{2}}if\Delta Q_{1}=Q_{2}$
then
$4 \Delta \text{t}_{2} = \Delta \text{t}_{1}$
$\Delta \text{t}_{2} = \Delta \text{t}_{1} / 4 = \frac{4}{4} = 1 min$