Heat transfer mechanisms problem; Conduction

[ctpengage]

Homework Statement

Diagram is attached showing part (a) and part (b)
Two identical rectangular rods of metal are welded end to end (a), with temperature of T1=0 0C on the left side and a temperature of T2=100 0C on the right hand side. In 2.0 minutes, 10J is conducted at a constant rate from the right side to left side. How much time would be required to conduct 10 J if the rods were welded side to side (b).

Homework Equations

P=kA(T₁-T₂) / L

The Attempt at a Solution

Now I know that the answer is 30 seconds or 1/4 of a minute. This means that the ratio of A/L for the first diagram is 4 times greater than the ratio of A/L for the second diagram, as the thermal conductivity and temperature difference is the same. However I have no idea how that result was achieved. Can anyone please provide me with help to find the solution.

 

[ctpengage]

please answer

 

[ekapil]

when the two metal rods are placed side to side , area of cross section together as -
new A = twice of previous A

and length is only the length of one length (length wise)

initially it was ..end to end ..so it was 2L
so..effective is the factor four

 

[RTW69]

In part "a" the rods are in series and in part "b" the rods are in parallel so you will need to review conduction in series and parallel pathways. q in part "a" is 10J/120 sec in part "b" q is 10J/ X sec. You have two equations set L/(K*A) = L/(K*A) and solve for T.

 

[RTW69]

OOPS! Sorry, solve for X in Seconds not T