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An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by?
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An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wal...
Introduction
To calculate the heat lost by the aluminum rod, we will use the formula for convection heat transfer. The rod is losing heat to the surrounding environment due to the temperature difference between the rod and the air.
Parameters
- Diameter of the rod (d): 2.0 cm = 0.02 m
- Radius (r): d/2 = 0.01 m
- Length of the rod (L): 12 cm = 0.12 m
- Temperature of the rod (T₁): 250°C
- Temperature of the environment (T₂): 15°C
- Convection heat-transfer coefficient (h): 12 W/m²·°C
Heat Loss Calculation
1. Surface Area (A):
The surface area of the cylindrical rod can be calculated using the formula:
\[ A = 2 \pi r L \]
\[ A = 2 \pi (0.01 m)(0.12 m) \]
\[ A \approx 0.00754 \, m² \]
2. Temperature Difference (ΔT):
\[ ΔT = T₁ - T₂ = 250°C - 15°C = 235°C \]
3. Heat Lost (Q):
The heat transfer rate can be calculated using:
\[ Q = h \cdot A \cdot ΔT \]
\[ Q = 12 \, W/m²·°C \cdot 0.00754 \, m² \cdot 235°C \]
\[ Q \approx 21.2 \, W \]
Conclusion
The heat lost by the aluminum rod to the environment is approximately 21.2 Watts. This value indicates how much thermal energy is being transferred away from the rod due to convection.
To calculate the heat lost by the aluminum rod, we will use the formula for convection heat transfer. The rod is losing heat to the surrounding environment due to the temperature difference between the rod and the air.
Parameters
- Diameter of the rod (d): 2.0 cm = 0.02 m
- Radius (r): d/2 = 0.01 m
- Length of the rod (L): 12 cm = 0.12 m
- Temperature of the rod (T₁): 250°C
- Temperature of the environment (T₂): 15°C
- Convection heat-transfer coefficient (h): 12 W/m²·°C
Heat Loss Calculation
1. Surface Area (A):
The surface area of the cylindrical rod can be calculated using the formula:
\[ A = 2 \pi r L \]
\[ A = 2 \pi (0.01 m)(0.12 m) \]
\[ A \approx 0.00754 \, m² \]
2. Temperature Difference (ΔT):
\[ ΔT = T₁ - T₂ = 250°C - 15°C = 235°C \]
3. Heat Lost (Q):
The heat transfer rate can be calculated using:
\[ Q = h \cdot A \cdot ΔT \]
\[ Q = 12 \, W/m²·°C \cdot 0.00754 \, m² \cdot 235°C \]
\[ Q \approx 21.2 \, W \]
Conclusion
The heat lost by the aluminum rod to the environment is approximately 21.2 Watts. This value indicates how much thermal energy is being transferred away from the rod due to convection.
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An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by?
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An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by?.
An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by?.
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