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Three rods of identical cross sectional area and made from the same metal from the sides of an isosceles triangle ABC right angled at B the points A and B are maintained at point at temperature t and √2t respectively in the steady state. assuming that only heat conduction takes place temperature of the point C will be?
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Three rods of identical cross sectional area and made from the same me...
Problem Statement
Three rods of identical cross sectional area and 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 temperatures t and √2t respectively in the steady state. Assuming that only heat conduction takes place, find the temperature of the point C.
Solution
In steady-state, the temperature gradient along each rod should be constant, and the heat flow through each rod should be equal. Let us assume that the rods are of length L.
Calculating Heat Flow
Let Q be the heat flow through each rod. The heat flow through a rod is given by:
Q = k * A * ΔT / L
Where k is the thermal conductivity of the metal, A is the cross-sectional area of the rod, ΔT is the temperature difference between the hot end and the cold end of the rod, and L is the length of the rod.
Since the rods have the same cross-sectional area and are made of the same metal, they have the same thermal conductivity, k, and cross-sectional area, A. Therefore, the heat flow through each rod is:
Q = k * A * ΔT / L = k * ΔT / L * A
Let us assume that the temperature of point C is T. Then, the temperature difference between point C and point A is ΔT1 = T - t, and the temperature difference between point C and point B is ΔT2 = T - √2t.
Since the heat flow through each rod is equal, we have:
k * ΔT1 / L * A = k * ΔT2 / L * A = Q
Simplifying this equation, we get:
ΔT1 = ΔT2
Therefore:
T - t = T - √2t
t = √2t
This is only possible if t = 0. Therefore, the temperature of point C is also 0.
Conclusion
The temperature of point C is 0.
Community Answer
Three rods of identical cross sectional area and made from the same me...
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Three rods of identical cross sectional area and made from the same metal from the sides of an isosceles triangle ABC right angled at B the points A and B are maintained at point at temperature t and √2t respectively in the steady state. assuming that only heat conduction takes place temperature of the point C will be?
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Three rods of identical cross sectional area and made from the same metal from the sides of an isosceles triangle ABC right angled at B the points A and B are maintained at point at temperature t and √2t respectively in the steady state. assuming that only heat conduction takes place temperature of the point C will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Three rods of identical cross sectional area and made from the same metal from the sides of an isosceles triangle ABC right angled at B the points A and B are maintained at point at temperature t and √2t respectively in the steady state. assuming that only heat conduction takes place temperature of the point C will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three rods of identical cross sectional area and made from the same metal from the sides of an isosceles triangle ABC right angled at B the points A and B are maintained at point at temperature t and √2t respectively in the steady state. assuming that only heat conduction takes place temperature of the point C will be?.
Three rods of identical cross sectional area and made from the same metal from the sides of an isosceles triangle ABC right angled at B the points A and B are maintained at point at temperature t and √2t respectively in the steady state. assuming that only heat conduction takes place temperature of the point C will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Three rods of identical cross sectional area and made from the same metal from the sides of an isosceles triangle ABC right angled at B the points A and B are maintained at point at temperature t and √2t respectively in the steady state. assuming that only heat conduction takes place temperature of the point C will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three rods of identical cross sectional area and made from the same metal from the sides of an isosceles triangle ABC right angled at B the points A and B are maintained at point at temperature t and √2t respectively in the steady state. assuming that only heat conduction takes place temperature of the point C will be?.
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