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Two long rods A and B of the same diameter have thermal conductivities k and 4 k and have attached by one side of their ends inserted into a furnace at 400 K. At a section 1 m away from the furnace, the temperature of rod B is 120°C. At what distance from the furnace end, the same temperature would be reached in the rod A?
  • a)
    0.2 m
  • b)
    0.25 m
  • c)
    0.5 m
  • d)
    0.75 m
Correct answer is option 'C'. Can you explain this answer?
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Two long rods A and B of the same diameter have thermal conductivities...

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Two long rods A and B of the same diameter have thermal conductivities...
In order to find the temperature of rod A at a section 1 m away from the furnace, we need to use the concept of thermal conductivity.

The rate of heat transfer through a rod can be calculated using the formula:

Q = (k * A * ΔT) / L

Where Q is the rate of heat transfer, k is the thermal conductivity, A is the cross-sectional area of the rod, ΔT is the temperature difference, and L is the length of the rod.

Given that rod B has a temperature of 120 K at a section 1 m away from the furnace, we can use this information to find the rate of heat transfer for rod B:

Q_B = (4k * A * ΔT_B) / L

Where Q_B is the rate of heat transfer for rod B and ΔT_B is the temperature difference for rod B.

Now, let's assume that rod A has a temperature of T_A at the same section 1 m away from the furnace. The rate of heat transfer for rod A can be calculated as:

Q_A = (k * A * ΔT_A) / L

Since both rods are attached at the end, the rate of heat transfer for rod A and rod B will be the same:

Q_A = Q_B

(k * A * ΔT_A) / L = (4k * A * ΔT_B) / L

Since the cross-sectional area and length of both rods are the same, we can cancel them out:

k * ΔT_A = 4k * ΔT_B

ΔT_A = 4 * ΔT_B

Now, we know that ΔT_B = 400 K - 120 K = 280 K. Substituting this value into the equation, we can solve for ΔT_A:

ΔT_A = 4 * 280 K = 1120 K

Finally, we can find the temperature of rod A at a section 1 m away from the furnace by adding the temperature difference to the temperature of rod B:

T_A = 120 K + 1120 K = 1240 K

Therefore, the temperature of rod A at a section 1 m away from the furnace is 1240 K.
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Two long rods A and B of the same diameter have thermal conductivities k and 4 kand have attached by one side of their ends inserted into a furnace at 400 K. At a section 1 m away from the furnace, the temperature of rod B is 120°C. At what distance from the furnace end, the same temperature would be reached in the rod A?a)0.2 mb)0.25 mc)0.5 md)0.75 mCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two long rods A and B of the same diameter have thermal conductivities k and 4 kand have attached by one side of their ends inserted into a furnace at 400 K. At a section 1 m away from the furnace, the temperature of rod B is 120°C. At what distance from the furnace end, the same temperature would be reached in the rod A?a)0.2 mb)0.25 mc)0.5 md)0.75 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two long rods A and B of the same diameter have thermal conductivities k and 4 kand have attached by one side of their ends inserted into a furnace at 400 K. At a section 1 m away from the furnace, the temperature of rod B is 120°C. At what distance from the furnace end, the same temperature would be reached in the rod A?a)0.2 mb)0.25 mc)0.5 md)0.75 mCorrect answer is option 'C'. Can you explain this answer?.
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