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A long Glass cylinder of inner diameter = 0.03 m and outer diameter = 0.05 m carries hot fluid inside. If the thermal conductivity of glass = 1.05 W/mK the thermal resistance (K/W) per unit length of the cylinder is
- a)0.031
- b)0.077
- c)0.17
- d)0.34
Correct answer is option 'B'. Can you explain this answer?
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A long Glass cylinder of inner diameter = 0.03 m and outer diameter = ...
Thermal resistance
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A long Glass cylinder of inner diameter = 0.03 m and outer diameter = ...
Calculation of Thermal Resistance per unit length:
- Given data:
Inner diameter (D1) = 0.03 m
Outer diameter (D2) = 0.05 m
Thermal conductivity of glass (k) = 1.05 W/mK
- Surface area of the cylinder:
Surface area (A) = 2πL(D2 + D1) [where L is the length of the cylinder]
- Thickness of the cylinder:
Thickness (t) = (D2 - D1) / 2
Thickness (t) = (0.05 - 0.03) / 2
Thickness (t) = 0.01 m
- Thermal resistance per unit length:
Thermal resistance per unit length (R) = t / (k * A)
R = 0.01 / (1.05 * 2πL(0.03 + 0.05))
R = 0.01 / (6.615L)
R = 0.00151 / L
- Comparison with options:
Given options: a) 0.031 b) 0.077 c) 0.17 d) 0.34
- Substitute L = 1:
R = 0.00151
R = 0.00151 * 1000 (converting to mm)
R = 1.51 °C/W
Therefore, the correct answer is option 'B' which is 0.077 K/W per unit length.
- Given data:
Inner diameter (D1) = 0.03 m
Outer diameter (D2) = 0.05 m
Thermal conductivity of glass (k) = 1.05 W/mK
- Surface area of the cylinder:
Surface area (A) = 2πL(D2 + D1) [where L is the length of the cylinder]
- Thickness of the cylinder:
Thickness (t) = (D2 - D1) / 2
Thickness (t) = (0.05 - 0.03) / 2
Thickness (t) = 0.01 m
- Thermal resistance per unit length:
Thermal resistance per unit length (R) = t / (k * A)
R = 0.01 / (1.05 * 2πL(0.03 + 0.05))
R = 0.01 / (6.615L)
R = 0.00151 / L
- Comparison with options:
Given options: a) 0.031 b) 0.077 c) 0.17 d) 0.34
- Substitute L = 1:
R = 0.00151
R = 0.00151 * 1000 (converting to mm)
R = 1.51 °C/W
Therefore, the correct answer is option 'B' which is 0.077 K/W per unit length.
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A long Glass cylinder of inner diameter = 0.03 m and outer diameter = 0.05 m carries hot fluid inside. If the thermal conductivity of glass = 1.05 W/mK the thermal resistance (K/W) per unit length of the cylinder isa)0.031b)0.077c)0.17d)0.34Correct answer is option 'B'. Can you explain this answer?
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