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Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be?
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Two rods, one of length l and the other of length 2l , are made of the...
Introduction:
In this scenario, we have two rods made of the same material and with the same diameter. One rod is of length 'l' and the other is of length '2l'. Both rods are exposed to the same environment at a temperature of 40°C. The ends of the longer rod are maintained at 100°C, while one end of the shorter rod is maintained at 100°C and the other end is insulated. We need to determine the temperature at the midpoint of the longer rod.
Concepts:
To solve this problem, we will consider the principles of heat transfer, specifically conduction. Heat transfer by conduction occurs when there is a temperature difference within a solid material, causing the heat to flow from higher temperature regions to lower temperature regions. The rate of heat transfer by conduction depends on the thermal conductivity of the material, the temperature difference, and the cross-sectional area.
Solution:
To find the temperature at the midpoint of the longer rod, we can analyze the heat flow through the rods and apply the principle of heat conduction.
1. Heat flow in the shorter rod:
- The end of the shorter rod maintained at 100°C acts as a heat source.
- Heat flows from the hot end towards the insulated end.
- At the insulated end, there is no heat exchange with the surroundings, so the temperature remains constant at 55°C.
- The temperature distribution along the shorter rod will be linear, with the highest temperature at the hot end and the lowest temperature at the insulated end.
2. Heat flow in the longer rod:
- The ends of the longer rod are maintained at 100°C, which act as heat sources.
- Heat flows from both ends towards the midpoint of the rod.
- The temperature distribution along the longer rod will also be linear, with the highest temperature at the ends and the lowest temperature at the midpoint.
3. Temperature at the midpoint of the longer rod:
- Since the shorter rod and the longer rod are made of the same material and have the same diameter, they have the same thermal conductivity.
- The temperature at the midpoint of the longer rod will be the average of the temperatures at the ends.
- Therefore, the temperature at the midpoint of the longer rod will be (100°C + 40°C) / 2 = 70°C.
Conclusion:
The temperature at the midpoint of the longer rod would be 70°C. This is because the heat flow in the longer rod is influenced by the temperature at both ends, and the temperature distribution is linear. By considering the principles of heat conduction, we can determine the temperature at different points along the rods.
In this scenario, we have two rods made of the same material and with the same diameter. One rod is of length 'l' and the other is of length '2l'. Both rods are exposed to the same environment at a temperature of 40°C. The ends of the longer rod are maintained at 100°C, while one end of the shorter rod is maintained at 100°C and the other end is insulated. We need to determine the temperature at the midpoint of the longer rod.
Concepts:
To solve this problem, we will consider the principles of heat transfer, specifically conduction. Heat transfer by conduction occurs when there is a temperature difference within a solid material, causing the heat to flow from higher temperature regions to lower temperature regions. The rate of heat transfer by conduction depends on the thermal conductivity of the material, the temperature difference, and the cross-sectional area.
Solution:
To find the temperature at the midpoint of the longer rod, we can analyze the heat flow through the rods and apply the principle of heat conduction.
1. Heat flow in the shorter rod:
- The end of the shorter rod maintained at 100°C acts as a heat source.
- Heat flows from the hot end towards the insulated end.
- At the insulated end, there is no heat exchange with the surroundings, so the temperature remains constant at 55°C.
- The temperature distribution along the shorter rod will be linear, with the highest temperature at the hot end and the lowest temperature at the insulated end.
2. Heat flow in the longer rod:
- The ends of the longer rod are maintained at 100°C, which act as heat sources.
- Heat flows from both ends towards the midpoint of the rod.
- The temperature distribution along the longer rod will also be linear, with the highest temperature at the ends and the lowest temperature at the midpoint.
3. Temperature at the midpoint of the longer rod:
- Since the shorter rod and the longer rod are made of the same material and have the same diameter, they have the same thermal conductivity.
- The temperature at the midpoint of the longer rod will be the average of the temperatures at the ends.
- Therefore, the temperature at the midpoint of the longer rod will be (100°C + 40°C) / 2 = 70°C.
Conclusion:
The temperature at the midpoint of the longer rod would be 70°C. This is because the heat flow in the longer rod is influenced by the temperature at both ends, and the temperature distribution is linear. By considering the principles of heat conduction, we can determine the temperature at different points along the rods.
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Two rods, one of length l and the other of length 2l , are made of the...
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Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be?
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Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be?.
Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be?.
Solutions for Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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Here you can find the meaning of Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be? defined & explained in the simplest way possible. Besides giving the explanation of
Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be?, a detailed solution for Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be? has been provided alongside types of Two rods, one of length l and the other of length 2l , are made of the same material and have same diameter. Both ends of the longer rod are maintained at 100 C. One end of the shorter rod is maintained at 100 C while the other end is insulated. Both rods are exposed to the same environment at 40C . The temperature at the insulated end is measured to be 55C . The temperature at the midpoint of the longer rod would be? theory, EduRev gives you an
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