Question

Two rods of same lengths, radii and material transfer a given amount of heat in 12 second when they are joined as shown in the figure (a). But when they are joined as shown in figure (b), then they will transfer same heat in same conditions in :

• A. 24 sec
• B. 13 sec
• C. 15 sec
• D. 48 sec

Answer 1

Answer: (D)

48 sec

As we know that, $Q=\frac{KA(T_1-T_2)\times t}{L}$
Now finding equivalent thermal resistance for series and parallel, we get
For series, $K_{equivalent}=K$
For parallel, $K_{equivalent}=2K$
Now both generate same heat so equating both of them, we find
$\frac{2K{t}_1}{L}=\frac{K{t}_2}{2L}$
So, $t_2=4\times t_1=48second$