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A cylindrical 70 tube of radius 0.05 cm and one CM has a wire embedded into it along its Axis to maintain a steady temperature difference of 140 degree Celsius between the inner and outer surfaces current of 5 ampere is made to flow into the wire assuming the resistance of wire as 0.1 % of length thermal conductivity of the cement would be dash watt per metre degree?
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A cylindrical 70 tube of radius 0.05 cm and one CM has a wire embedded...
Calculation of Thermal Conductivity of Cement
Given Data:
- Length of tube, L = 1 cm
- Radius of tube, r = 0.05 cm
- Temperature difference, ΔT = 140°C
- Current in wire, I = 5 A
- Resistance of wire, R = 0.1% of L
Calculation of Heat Transfer Rate:
The heat transfer rate through the tube can be calculated using the following formula:
Q = 2πrLkΔT
- Where, k is the thermal conductivity of the cement.
Substituting the given values in the above equation, we get:
Q = 2π(0.05)(1)(k)(140)
Q = 0.44k
Calculation of Power Dissipated by Wire:
The power dissipated by the wire can be calculated using the following formula:
P = I²R
Substituting the given values in the above equation, we get:
P = (5)²(0.1/100)(1)
P = 0.0025 W
Equating Heat Transfer Rate and Power Dissipated by Wire:
Since the heat transfer rate through the tube must be equal to the power dissipated by the wire, we can equate the two values:
0.44k = 0.0025
k = 0.0057 W/m°C
Explanation:
The given problem involves calculating the thermal conductivity of a cement used in a cylindrical tube with a wire embedded along its axis. The wire is used to maintain a steady temperature difference of 140°C between the inner and outer surfaces of the tube. A current of 5 A is made to flow through the wire, and the resistance of the wire is given as 0.1% of the length of the tube. Using the formula for heat transfer rate through a cylindrical tube, we can calculate the heat transfer rate from the inner surface to the outer surface of the tube. Equating this heat transfer rate to the power dissipated by the wire, we can solve for the thermal conductivity of the cement. The final answer is 0.0057 W/m°C.
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A cylindrical 70 tube of radius 0.05 cm and one CM has a wire embedded into it along its Axis to maintain a steady temperature difference of 140 degree Celsius between the inner and outer surfaces current of 5 ampere is made to flow into the wire assuming the resistance of wire as 0.1 % of length thermal conductivity of the cement would be dash watt per metre degree?
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A cylindrical 70 tube of radius 0.05 cm and one CM has a wire embedded into it along its Axis to maintain a steady temperature difference of 140 degree Celsius between the inner and outer surfaces current of 5 ampere is made to flow into the wire assuming the resistance of wire as 0.1 % of length thermal conductivity of the cement would be dash watt per metre degree? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cylindrical 70 tube of radius 0.05 cm and one CM has a wire embedded into it along its Axis to maintain a steady temperature difference of 140 degree Celsius between the inner and outer surfaces current of 5 ampere is made to flow into the wire assuming the resistance of wire as 0.1 % of length thermal conductivity of the cement would be dash watt per metre degree? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical 70 tube of radius 0.05 cm and one CM has a wire embedded into it along its Axis to maintain a steady temperature difference of 140 degree Celsius between the inner and outer surfaces current of 5 ampere is made to flow into the wire assuming the resistance of wire as 0.1 % of length thermal conductivity of the cement would be dash watt per metre degree?.
A cylindrical 70 tube of radius 0.05 cm and one CM has a wire embedded into it along its Axis to maintain a steady temperature difference of 140 degree Celsius between the inner and outer surfaces current of 5 ampere is made to flow into the wire assuming the resistance of wire as 0.1 % of length thermal conductivity of the cement would be dash watt per metre degree? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cylindrical 70 tube of radius 0.05 cm and one CM has a wire embedded into it along its Axis to maintain a steady temperature difference of 140 degree Celsius between the inner and outer surfaces current of 5 ampere is made to flow into the wire assuming the resistance of wire as 0.1 % of length thermal conductivity of the cement would be dash watt per metre degree? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical 70 tube of radius 0.05 cm and one CM has a wire embedded into it along its Axis to maintain a steady temperature difference of 140 degree Celsius between the inner and outer surfaces current of 5 ampere is made to flow into the wire assuming the resistance of wire as 0.1 % of length thermal conductivity of the cement would be dash watt per metre degree?.
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