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104. In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. K 2K Furnace 300°C Metal I Metal 11 lce box 0 deg * C Insulation The coefficient of thermal conductivities of the metals are K and 2K, respectively. If the furnace temperature?
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104. In the diagram, a system of two metals of equal lengths and of sa...
Understanding the Heat Transfer in the System
In this scenario, we have two metals connected in series, one with thermal conductivity K and the other with 2K. The temperature differential between the furnace (300°C) and the ice box (0°C) creates a heat flow through both metals.
Heat Transfer Basics
- The heat transfer (Q) through a material is governed by Fourier's law:
where k is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference, and L is the length of the material.
Temperature Gradient
- The system's steady-state temperature gradient will depend on the thermal resistances of both metals:
- The total thermal resistance (R_total) is:
Calculating the Temperature at the Junction
- The effective thermal resistance indicates that more heat will flow through Metal II due to its higher conductivity. The temperature at the junction (T_j) between the two metals can be found using the heat balance:
- By solving these equations, you can derive the temperature at the junction, which will be closer to the furnace temperature due to the higher conductivity of Metal II.
Conclusion
- The final temperature at the junction will be influenced heavily by the thermal conductivities of the metals, emphasizing the role of material properties in thermal systems.
In this scenario, we have two metals connected in series, one with thermal conductivity K and the other with 2K. The temperature differential between the furnace (300°C) and the ice box (0°C) creates a heat flow through both metals.
Heat Transfer Basics
- The heat transfer (Q) through a material is governed by Fourier's law:
Q = k * A * (ΔT/L)
where k is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference, and L is the length of the material.
Temperature Gradient
- The system's steady-state temperature gradient will depend on the thermal resistances of both metals:
R1 = L/(K * A) for Metal I
R2 = L/(2K * A) for Metal II
- The total thermal resistance (R_total) is:
R_total = R1 + R2 = (L/(K * A)) + (L/(2K * A))
Calculating the Temperature at the Junction
- The effective thermal resistance indicates that more heat will flow through Metal II due to its higher conductivity. The temperature at the junction (T_j) between the two metals can be found using the heat balance:
Q = (T_furnace - T_j)/R1 = (T_j - T_icebox)/R2
- By solving these equations, you can derive the temperature at the junction, which will be closer to the furnace temperature due to the higher conductivity of Metal II.
Conclusion
- The final temperature at the junction will be influenced heavily by the thermal conductivities of the metals, emphasizing the role of material properties in thermal systems.
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104. In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. K 2K Furnace 300°C Metal I Metal 11 lce box 0 deg * C Insulation The coefficient of thermal conductivities of the metals are K and 2K, respectively. If the furnace temperature?
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104. In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. K 2K Furnace 300°C Metal I Metal 11 lce box 0 deg * C Insulation The coefficient of thermal conductivities of the metals are K and 2K, respectively. If the furnace temperature? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 104. In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. K 2K Furnace 300°C Metal I Metal 11 lce box 0 deg * C Insulation The coefficient of thermal conductivities of the metals are K and 2K, respectively. If the furnace temperature? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 104. In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. K 2K Furnace 300°C Metal I Metal 11 lce box 0 deg * C Insulation The coefficient of thermal conductivities of the metals are K and 2K, respectively. If the furnace temperature?.
104. In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. K 2K Furnace 300°C Metal I Metal 11 lce box 0 deg * C Insulation The coefficient of thermal conductivities of the metals are K and 2K, respectively. If the furnace temperature? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 104. In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. K 2K Furnace 300°C Metal I Metal 11 lce box 0 deg * C Insulation The coefficient of thermal conductivities of the metals are K and 2K, respectively. If the furnace temperature? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 104. In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. K 2K Furnace 300°C Metal I Metal 11 lce box 0 deg * C Insulation The coefficient of thermal conductivities of the metals are K and 2K, respectively. If the furnace temperature?.
Solutions for 104. In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. K 2K Furnace 300°C Metal I Metal 11 lce box 0 deg * C Insulation The coefficient of thermal conductivities of the metals are K and 2K, respectively. If the furnace temperature? in English & in Hindi are available as part of our courses for UPSC.
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