question_answer

             Two rods of same material have same length and area. The heat \[\Delta Q\] flows through them for 12 minutes 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

Correct Answer: B

Solution :

When rods are joined in series then heat flow \[\Delta {{Q}_{1}}=\frac{A({{T}_{1}}-{{T}_{2}}){{t}_{1}}}{\frac{{{l}_{1}}}{{{K}_{1}}}+\frac{{{l}_{1}}}{{{K}_{2}}}}\] \[=\frac{A({{T}_{1}}-{{T}_{2}}){{t}_{1}}}{\frac{l}{{{K}_{1}}}+\frac{l}{{{K}_{2}}}}=\frac{A({{T}_{1}}-{{T}_{2}}){{t}_{1}}}{l}=\frac{K}{2}\] When rods are joined in parallel \[\Delta {{Q}_{2}}=({{K}_{1}}A+{{K}_{2}}A)\frac{({{T}_{1}}-{{T}_{2}}){{t}_{2}}}{l}\] \[=\frac{2KA({{T}_{1}}-{{T}_{2}}){{t}_{2}}}{l}\] \[\because \]     \[\Delta {{Q}_{1}}=\Delta {{Q}_{2}}\]                      (given) \[\therefore \]  \[{{t}_{2}}=\frac{{{t}_{1}}}{4}=\frac{12}{4}=3\min \]