Heat Flow in Three Identical Rods of Metal

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Homework Help Overview

The problem involves three rods of identical cross-sectional area made from the same metal, forming the sides of an isosceles triangle ABC, which is right-angled at B. The temperatures at points A and B are maintained at T and √2 T, respectively, in a steady state, with heat conduction as the only mode of heat transfer.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the relationships between the rates of heat flow in the rods and the temperature gradients across them. There is an attempt to calculate the temperature at point C, with some questioning the correctness of the calculations and the assumptions about the triangle's geometry.

Discussion Status

The discussion is ongoing, with some participants providing calculations and others questioning the setup and assumptions. There is no explicit consensus on the correctness of the original poster's statements, and multiple interpretations of the problem are being explored.

Contextual Notes

Some participants express confusion regarding the geometry of the triangle, specifically whether it can be isosceles and right-angled at B. There are also indications that the calculations regarding the temperature at point C may be under scrutiny.

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Homework Statement


Three rods of identical cross-sectional area are made from the same metal, form the sides of an isosceles triangle ABC right angled at B. The points A and B are maintained at temperature T and √2 T respectively in steady state. Assume that only heat conduction takes place. Then

a) Rate of heat flow in BA is equal to rate of heat flow in CA

b) Temperature gradient across CA is equal to the temperature gradient across BA


The Attempt at a Solution



I got the temperature at C as 3T/1+√2.

Temperature at B > Temperature at A.
Rate of flow in BA will be equal to the rate of heat flow in BCA (not CA)
Again temperature gradient will be same across BCA

Both a and b are correct. I don't understand how. Help.
 
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Abdul Quadeer said:

Homework Statement


Three rods of identical cross-sectional area are made from the same metal, form the sides of an isosceles triangle ABC right angled at B.
How can isosceles triangle ABC be right angled at B?
 
Your calculation of temperature at C is wrong.
The two statements are true for BA and BC, rather BA and CA.
Check the problem.
 
How can isosceles triangle ABC be right angled at B?

Take a look at the figure.

Your calculation of temperature at C is wrong.

I found the temperature at C by equating the rate of heat flow through BC and CA.
I got the same answer after checking.
 

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