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Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton is
- a)30°C
- b)40°C
- c)50°C
- d)60°C
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Two metal rods A and B of equal lengths and equal cross sectional area...
Answer for this question is b) as their length and cross sectional area are same and their thermal conductivities are also in ratio so we can directly compare their heat current I.e Q/t
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Most Upvoted Answer
Two metal rods A and B of equal lengths and equal cross sectional area...
Understanding the Problem
Two rods, A and B, are connected end to end with different thermal conductivities. The goal is to find the temperature at the junction when one end of rod A is at 100°C and the other end of rod B is at 0°C.
Given Data
- Lengths of rods A and B: Equal
- Cross-sectional areas: Equal
- Coefficients of thermal conductivity ratio: 2:3 (A:B)
- Temperature at free end of A: 100°C
- Temperature at free end of B: 0°C
Heat Transfer through Rods
Using the principle of steady-state heat transfer, the rate of heat flow (Q) through both rods must be equal. The equation for heat transfer is given by:
Q = k * A * (T1 - T2) / L
Where:
- k = thermal conductivity
- A = cross-sectional area
- T1 and T2 = temperatures at the ends
- L = length of the rod
Since both rods are of equal length and area, we can simplify the equation.
Setting Up the Equation
Let the temperature at the junction be T.
For rod A:
- Q_A = (2 * (100 - T)) / L
For rod B:
- Q_B = (3 * (T - 0)) / L
Setting Q_A = Q_B:
2 * (100 - T) = 3 * T
Solving for T
Expanding the equation:
200 - 2T = 3T
Combining like terms:
200 = 5T
Thus, T = 40°C.
Conclusion
The temperature at the junction of rods A and B is 40°C, making the correct answer option B.
Two rods, A and B, are connected end to end with different thermal conductivities. The goal is to find the temperature at the junction when one end of rod A is at 100°C and the other end of rod B is at 0°C.
Given Data
- Lengths of rods A and B: Equal
- Cross-sectional areas: Equal
- Coefficients of thermal conductivity ratio: 2:3 (A:B)
- Temperature at free end of A: 100°C
- Temperature at free end of B: 0°C
Heat Transfer through Rods
Using the principle of steady-state heat transfer, the rate of heat flow (Q) through both rods must be equal. The equation for heat transfer is given by:
Q = k * A * (T1 - T2) / L
Where:
- k = thermal conductivity
- A = cross-sectional area
- T1 and T2 = temperatures at the ends
- L = length of the rod
Since both rods are of equal length and area, we can simplify the equation.
Setting Up the Equation
Let the temperature at the junction be T.
For rod A:
- Q_A = (2 * (100 - T)) / L
For rod B:
- Q_B = (3 * (T - 0)) / L
Setting Q_A = Q_B:
2 * (100 - T) = 3 * T
Solving for T
Expanding the equation:
200 - 2T = 3T
Combining like terms:
200 = 5T
Thus, T = 40°C.
Conclusion
The temperature at the junction of rods A and B is 40°C, making the correct answer option B.
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Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton isa)30°Cb)40°Cc)50°Cd)60°CCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton isa)30°Cb)40°Cc)50°Cd)60°CCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton isa)30°Cb)40°Cc)50°Cd)60°CCorrect answer is option 'B'. Can you explain this answer?.
Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton isa)30°Cb)40°Cc)50°Cd)60°CCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton isa)30°Cb)40°Cc)50°Cd)60°CCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton isa)30°Cb)40°Cc)50°Cd)60°CCorrect answer is option 'B'. Can you explain this answer?.
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Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton isa)30°Cb)40°Cc)50°Cd)60°CCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton isa)30°Cb)40°Cc)50°Cd)60°CCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Two metal rods A and B of equal lengths and equal cross sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3 when the free end of A is maintained at 100°C and the free end of B is maintained at 0°C, the temprature of the junciton isa)30°Cb)40°Cc)50°Cd)60°CCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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