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The ratio of the coefficient thermal conductivity of two different materials is 5 : 3. If the thermal
resistance of the rods of same thickness of these materials is same, then the ratio of the length of
these rods will be -
resistance of the rods of same thickness of these materials is same, then the ratio of the length of
these rods will be -
- a)3 : 5
- b)5 : 3
- c)3 : 4
- d)3 : 2
Correct answer is option 'B'. Can you explain this answer?
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The ratio of the coefficient thermal conductivity of two different mat...
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Concept:
The thermal resistance of a material is directly proportional to its length and inversely proportional to its thermal conductivity. Mathematically, the thermal resistance (R) of a material is given by R = L / k, where L is the length of the material and k is the thermal conductivity.
Solution:
Let the lengths of the two rods be L1 and L2, and their thermal conductivities be k1 and k2 respectively.
Given that the ratio of the thermal conductivities is 5 : 3, we can write k1 : k2 = 5 : 3.
Since the thermal resistance of the rods is the same, we have L1 / k1 = L2 / k2.
Substitute the ratios of k1 and k2 into the equation above, we get L1 / 5 = L2 / 3.
Cross multiplying, we get 3L1 = 5L2.
Therefore, the ratio of the lengths of the rods is 3 : 5, which corresponds to option B.
The thermal resistance of a material is directly proportional to its length and inversely proportional to its thermal conductivity. Mathematically, the thermal resistance (R) of a material is given by R = L / k, where L is the length of the material and k is the thermal conductivity.
Solution:
Let the lengths of the two rods be L1 and L2, and their thermal conductivities be k1 and k2 respectively.
Given that the ratio of the thermal conductivities is 5 : 3, we can write k1 : k2 = 5 : 3.
Since the thermal resistance of the rods is the same, we have L1 / k1 = L2 / k2.
Substitute the ratios of k1 and k2 into the equation above, we get L1 / 5 = L2 / 3.
Cross multiplying, we get 3L1 = 5L2.
Therefore, the ratio of the lengths of the rods is 3 : 5, which corresponds to option B.
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The ratio of the coefficient thermal conductivity of two different materials is 5 : 3. If the thermalresistance of the rods of same thickness of these materials is same, then the ratio of the length ofthese rods will be -a)3 : 5b)5 : 3c)3 : 4d)3 : 2Correct answer is option 'B'. Can you explain this answer?
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