Question

Two rods of same material have same length and area. The heat $\Delta Q$ flows through them for $12min$ when they are joint side by side. If now both the rods are joined in parallel, then the same amount of heat $\Delta Q$ will flow in:

• A. 24 min
• B. 3 min
• C. 12 min
• D. 6 min

Answer 1

Answer: (B)

When two rods are joined, then the rate of flow of heat is given by
$Q=KA\frac{({\theta }_1-{\theta }_2)}{l}t$
where K is coefficient of thermal conductivity, A is area and I is length when rods are joined in series.
$\Delta Q_1=\frac{A(T_1-T_2)t_1}{\frac{l_1}{K_1}+\frac{l_2}{K_2}}$
Given, $l_1=l_2=l,K_1=K_2=K,$
we have $\Delta Q_1=\frac{A(T_1-T_2)t_1}{\frac{l}{K_1}+\frac{l}{K_2}}$
$=\frac{A(T_1-T_2)t_1}{l}\frac{K}{2}$
when rods are joined in parallel
$\Delta Q_2=(K_{1}A+K_{2}A)\frac{(T_1-T_2)t_2}{l}$
$=2\frac{KA(T_1-T_2)t_2}{l}$
Given, $\Delta Q_1=\Delta Q_2$
$\therefore$ $t_2=\frac{t_1}{4}=\frac{12}{4}=3\min$