Heat transfer mechanisms problem; Conduction

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Homework Help Overview

The problem involves heat transfer mechanisms, specifically conduction, between two identical rectangular metal rods. The scenario compares heat conduction when the rods are arranged end to end versus side by side, with specific temperatures and a given amount of heat transferred over time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the implications of the rods' arrangement on heat conduction, noting the differences between series and parallel configurations. There are attempts to derive relationships between the areas and lengths involved in the two setups.

Discussion Status

Some participants have provided insights into the equations governing heat conduction and the factors affecting the rate of heat transfer. There is ongoing exploration of how to relate the two scenarios mathematically, with no explicit consensus reached on the final solution.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. The original poster expresses uncertainty about how to arrive at a specific result based on their understanding of the problem.

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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.
 

Attachments

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please answer
 
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
 
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.
 
OOPS! Sorry, solve for X in Seconds not T
 

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