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In the following figure, two insulating sheets with thermal resistances R and 3R as shown in figure. The temperature 0 is: Q 20 deg * C 3R 0 R 100 deg * C Q (a) 20 deg * C (b) 60 deg * C (c) 75 deg * C (d) 80 deg * C?
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In the following figure, two insulating sheets with thermal resistance...
Understanding the Problem
In this thermal resistance problem, we have two insulating sheets with thermal resistances R and 3R. The temperatures at the two ends are given as 100°C and 20°C, respectively. We need to find the temperature at the interface (T0) between the two sheets.
Thermal Resistance Analysis
- The thermal resistances are arranged in series. The total thermal resistance (R_total) can be calculated as:
R_total = R + 3R = 4R
- Using the concept of heat transfer (Q), we can express it as:
Q = (T1 - T2) / R_total
Here, T1 = 100°C (hot side) and T2 = 20°C (cold side).
Calculating Heat Transfer (Q)
- Substitute the values:
Q = (100°C - 20°C) / 4R = 80°C / 4R = 20 / R
Temperature at the Interface (T0)
- The heat flow through each thermal resistance is the same. To find T0, we can use the thermal resistance of R:
Q = (T1 - T0) / R
- Rearranging gives:
T1 - T0 = Q * R
- Substitute Q:
T1 - T0 = (20 / R) * R = 20
- Therefore:
T0 = T1 - 20 = 100°C - 20 = 80°C
Conclusion
The temperature at the interface (T0) is 80°C. Therefore, the correct answer is:
(d) 80 deg * C
In this thermal resistance problem, we have two insulating sheets with thermal resistances R and 3R. The temperatures at the two ends are given as 100°C and 20°C, respectively. We need to find the temperature at the interface (T0) between the two sheets.
Thermal Resistance Analysis
- The thermal resistances are arranged in series. The total thermal resistance (R_total) can be calculated as:
R_total = R + 3R = 4R
- Using the concept of heat transfer (Q), we can express it as:
Q = (T1 - T2) / R_total
Here, T1 = 100°C (hot side) and T2 = 20°C (cold side).
Calculating Heat Transfer (Q)
- Substitute the values:
Q = (100°C - 20°C) / 4R = 80°C / 4R = 20 / R
Temperature at the Interface (T0)
- The heat flow through each thermal resistance is the same. To find T0, we can use the thermal resistance of R:
Q = (T1 - T0) / R
- Rearranging gives:
T1 - T0 = Q * R
- Substitute Q:
T1 - T0 = (20 / R) * R = 20
- Therefore:
T0 = T1 - 20 = 100°C - 20 = 80°C
Conclusion
The temperature at the interface (T0) is 80°C. Therefore, the correct answer is:
(d) 80 deg * C
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In the following figure, two insulating sheets with thermal resistances R and 3R as shown in figure. The temperature 0 is: Q 20 deg * C 3R 0 R 100 deg * C Q (a) 20 deg * C (b) 60 deg * C (c) 75 deg * C (d) 80 deg * C?
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In the following figure, two insulating sheets with thermal resistances R and 3R as shown in figure. The temperature 0 is: Q 20 deg * C 3R 0 R 100 deg * C Q (a) 20 deg * C (b) 60 deg * C (c) 75 deg * C (d) 80 deg * C? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the following figure, two insulating sheets with thermal resistances R and 3R as shown in figure. The temperature 0 is: Q 20 deg * C 3R 0 R 100 deg * C Q (a) 20 deg * C (b) 60 deg * C (c) 75 deg * C (d) 80 deg * C? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following figure, two insulating sheets with thermal resistances R and 3R as shown in figure. The temperature 0 is: Q 20 deg * C 3R 0 R 100 deg * C Q (a) 20 deg * C (b) 60 deg * C (c) 75 deg * C (d) 80 deg * C?.
In the following figure, two insulating sheets with thermal resistances R and 3R as shown in figure. The temperature 0 is: Q 20 deg * C 3R 0 R 100 deg * C Q (a) 20 deg * C (b) 60 deg * C (c) 75 deg * C (d) 80 deg * C? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the following figure, two insulating sheets with thermal resistances R and 3R as shown in figure. The temperature 0 is: Q 20 deg * C 3R 0 R 100 deg * C Q (a) 20 deg * C (b) 60 deg * C (c) 75 deg * C (d) 80 deg * C? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following figure, two insulating sheets with thermal resistances R and 3R as shown in figure. The temperature 0 is: Q 20 deg * C 3R 0 R 100 deg * C Q (a) 20 deg * C (b) 60 deg * C (c) 75 deg * C (d) 80 deg * C?.
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