Question

Two rods of same material have same length and area. The heat $\Delta Q$ flows through them for $12\, min$ 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)

3 min

Answer 2

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, $\Delta {{Q}_{1}}=\Delta {{Q}_{2}}$
$\therefore$ ${{t}_{2}}=\frac{{{t}_{1}}}{4}=\frac{12}{4}=3\,\min$