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Four cylindrical rods of different radii and lengths are used to connect two heat reservoirs at fixed temperatures t1 and t2 respectively. From the following pick out the rod which will conduct the maximum quantity of heat:
- a)Radius 1 cm, length 2 m
- b)Radius 1 cm, length 1 m
- c)Radius 2 cm, length 4 m
- d)Radius 3 cm, length 8 m
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Four cylindrical rods of different radii and lengths are used to conne...
The rate of heat transfer is directly proportional to the bisectional surface area of the solid and inversely proportional to its parallel length.
That is heat conduction rate say H ∝ r2
∝ 1/L
I.e ∝ r2/L
Hence the conduction would be
maximum in case in which r2/L ratio is largest.
That is heat conduction rate say H ∝ r2
∝ 1/L
I.e ∝ r2/L
Hence the conduction would be
maximum in case in which r2/L ratio is largest.
Most Upvoted Answer
Four cylindrical rods of different radii and lengths are used to conne...
Explanation:
The rate of heat transfer through a rod is given by the formula:
Q/t = kA(T1-T2)/L
where Q is the heat transferred, t is time, k is the thermal conductivity of the material, A is the cross-sectional area of the rod, T1 and T2 are the temperatures at the ends of the rod, and L is the length of the rod.
Comparison of the rods:
a) Radius 1 cm, length 2 m
- Cross-sectional area (A) = πr^2 = 3.14 cm^2
- Length (L) = 2 m
b) Radius 1 cm, length 1 m
- Cross-sectional area (A) = πr^2 = 3.14 cm^2
- Length (L) = 1 m
c) Radius 2 cm, length 4 m
- Cross-sectional area (A) = πr^2 = 12.56 cm^2
- Length (L) = 4 m
d) Radius 3 cm, length 8 m
- Cross-sectional area (A) = πr^2 = 28.27 cm^2
- Length (L) = 8 m
Calculation:
Assuming all the rods are made up of the same material, we can compare their rates of heat transfer by comparing the values of kA/L.
a) kA/L = (0.02 W/m.K) x 3.14 cm^2 / 2 m = 0.010 W/K
b) kA/L = (0.02 W/m.K) x 3.14 cm^2 / 1 m = 0.020 W/K
c) kA/L = (0.02 W/m.K) x 12.56 cm^2 / 4 m = 0.063 W/K
d) kA/L = (0.02 W/m.K) x 28.27 cm^2 / 8 m = 0.079 W/K
Therefore, the rod with the highest value of kA/L will conduct the maximum quantity of heat. In this case, it is the rod with radius 3 cm and length 8 m (option D).
Conclusion:
Hence, option D is the correct answer.
The rate of heat transfer through a rod is given by the formula:
Q/t = kA(T1-T2)/L
where Q is the heat transferred, t is time, k is the thermal conductivity of the material, A is the cross-sectional area of the rod, T1 and T2 are the temperatures at the ends of the rod, and L is the length of the rod.
Comparison of the rods:
a) Radius 1 cm, length 2 m
- Cross-sectional area (A) = πr^2 = 3.14 cm^2
- Length (L) = 2 m
b) Radius 1 cm, length 1 m
- Cross-sectional area (A) = πr^2 = 3.14 cm^2
- Length (L) = 1 m
c) Radius 2 cm, length 4 m
- Cross-sectional area (A) = πr^2 = 12.56 cm^2
- Length (L) = 4 m
d) Radius 3 cm, length 8 m
- Cross-sectional area (A) = πr^2 = 28.27 cm^2
- Length (L) = 8 m
Calculation:
Assuming all the rods are made up of the same material, we can compare their rates of heat transfer by comparing the values of kA/L.
a) kA/L = (0.02 W/m.K) x 3.14 cm^2 / 2 m = 0.010 W/K
b) kA/L = (0.02 W/m.K) x 3.14 cm^2 / 1 m = 0.020 W/K
c) kA/L = (0.02 W/m.K) x 12.56 cm^2 / 4 m = 0.063 W/K
d) kA/L = (0.02 W/m.K) x 28.27 cm^2 / 8 m = 0.079 W/K
Therefore, the rod with the highest value of kA/L will conduct the maximum quantity of heat. In this case, it is the rod with radius 3 cm and length 8 m (option D).
Conclusion:
Hence, option D is the correct answer.
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Four cylindrical rods of different radii and lengths are used to connect two heat reservoirs at fixed temperatures t1and t2respectively. From the following pick out the rod which will conduct the maximum quantity of heat:a)Radius 1 cm, length 2 mb)Radius 1 cm, length 1 mc)Radius 2 cm, length 4 md)Radius 3 cm, length 8 mCorrect answer is option 'D'. Can you explain this answer?
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Four cylindrical rods of different radii and lengths are used to connect two heat reservoirs at fixed temperatures t1and t2respectively. From the following pick out the rod which will conduct the maximum quantity of heat:a)Radius 1 cm, length 2 mb)Radius 1 cm, length 1 mc)Radius 2 cm, length 4 md)Radius 3 cm, length 8 mCorrect answer is option 'D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Four cylindrical rods of different radii and lengths are used to connect two heat reservoirs at fixed temperatures t1and t2respectively. From the following pick out the rod which will conduct the maximum quantity of heat:a)Radius 1 cm, length 2 mb)Radius 1 cm, length 1 mc)Radius 2 cm, length 4 md)Radius 3 cm, length 8 mCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four cylindrical rods of different radii and lengths are used to connect two heat reservoirs at fixed temperatures t1and t2respectively. From the following pick out the rod which will conduct the maximum quantity of heat:a)Radius 1 cm, length 2 mb)Radius 1 cm, length 1 mc)Radius 2 cm, length 4 md)Radius 3 cm, length 8 mCorrect answer is option 'D'. Can you explain this answer?.
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