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A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, then
- a)Both spheres will cool at the same rate for small values of T
- b)Both spheres will cool at the same reactor small values of T
- c)The hollow sphere will cool at a faster rate for all the values of T
- d)The solid sphere will cool a faster rate for all the values of T
Correct answer is option 'C'. Can you explain this answer?
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Introduction:
The question compares the cooling rates of a solid sphere and a hollow sphere of the same material and size when they are heated to the same temperature and allowed to cool in the same surroundings. The temperature difference between the body and the surroundings is denoted by T.
Explanation:
To understand why the hollow sphere cools at a faster rate for all values of T, we need to consider the factors that affect the rate of cooling.
Surface Area:
The rate of heat transfer is directly proportional to the surface area. In the case of a hollow sphere, the outer surface area is larger compared to a solid sphere of the same size. This means that the hollow sphere has a larger surface area available for heat transfer, resulting in a faster cooling rate.
Thickness of Material:
The rate of heat transfer through a material is inversely proportional to its thickness. In the case of a hollow sphere, the material thickness is less compared to a solid sphere of the same size. This means that the hollow sphere allows heat to transfer more easily, leading to a faster cooling rate.
Hollow Space:
The hollow space in the hollow sphere acts as an insulating layer, reducing the heat transfer from the inner surface to the outer surface. This means that the inner surface of the hollow sphere will cool down more slowly compared to the outer surface. As a result, the temperature difference between the inner and outer surface of the hollow sphere is larger, leading to a faster cooling rate.
Conclusion:
In conclusion, the hollow sphere cools at a faster rate for all values of T due to its larger surface area, thinner material thickness, and the presence of a hollow space. These factors facilitate more efficient heat transfer, resulting in a faster rate of cooling compared to the solid sphere.
The question compares the cooling rates of a solid sphere and a hollow sphere of the same material and size when they are heated to the same temperature and allowed to cool in the same surroundings. The temperature difference between the body and the surroundings is denoted by T.
Explanation:
To understand why the hollow sphere cools at a faster rate for all values of T, we need to consider the factors that affect the rate of cooling.
Surface Area:
The rate of heat transfer is directly proportional to the surface area. In the case of a hollow sphere, the outer surface area is larger compared to a solid sphere of the same size. This means that the hollow sphere has a larger surface area available for heat transfer, resulting in a faster cooling rate.
Thickness of Material:
The rate of heat transfer through a material is inversely proportional to its thickness. In the case of a hollow sphere, the material thickness is less compared to a solid sphere of the same size. This means that the hollow sphere allows heat to transfer more easily, leading to a faster cooling rate.
Hollow Space:
The hollow space in the hollow sphere acts as an insulating layer, reducing the heat transfer from the inner surface to the outer surface. This means that the inner surface of the hollow sphere will cool down more slowly compared to the outer surface. As a result, the temperature difference between the inner and outer surface of the hollow sphere is larger, leading to a faster cooling rate.
Conclusion:
In conclusion, the hollow sphere cools at a faster rate for all values of T due to its larger surface area, thinner material thickness, and the presence of a hollow space. These factors facilitate more efficient heat transfer, resulting in a faster rate of cooling compared to the solid sphere.
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A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, thena)Both spheres will cool at the same rate for small values of Tb)Both spheres will cool at the same reactor small values of Tc)The hollow sphere will cool at a faster rate for all the values of Td)The solid sphere will cool a faster rate for all the values of TCorrect answer is option 'C'. Can you explain this answer?
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A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, thena)Both spheres will cool at the same rate for small values of Tb)Both spheres will cool at the same reactor small values of Tc)The hollow sphere will cool at a faster rate for all the values of Td)The solid sphere will cool a faster rate for all the values of TCorrect answer is option 'C'. Can you explain this answer? 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 A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, thena)Both spheres will cool at the same rate for small values of Tb)Both spheres will cool at the same reactor small values of Tc)The hollow sphere will cool at a faster rate for all the values of Td)The solid sphere will cool a faster rate for all the values of TCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, thena)Both spheres will cool at the same rate for small values of Tb)Both spheres will cool at the same reactor small values of Tc)The hollow sphere will cool at a faster rate for all the values of Td)The solid sphere will cool a faster rate for all the values of TCorrect answer is option 'C'. Can you explain this answer?.
A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, thena)Both spheres will cool at the same rate for small values of Tb)Both spheres will cool at the same reactor small values of Tc)The hollow sphere will cool at a faster rate for all the values of Td)The solid sphere will cool a faster rate for all the values of TCorrect answer is option 'C'. Can you explain this answer? 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 A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, thena)Both spheres will cool at the same rate for small values of Tb)Both spheres will cool at the same reactor small values of Tc)The hollow sphere will cool at a faster rate for all the values of Td)The solid sphere will cool a faster rate for all the values of TCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, thena)Both spheres will cool at the same rate for small values of Tb)Both spheres will cool at the same reactor small values of Tc)The hollow sphere will cool at a faster rate for all the values of Td)The solid sphere will cool a faster rate for all the values of TCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, thena)Both spheres will cool at the same rate for small values of Tb)Both spheres will cool at the same reactor small values of Tc)The hollow sphere will cool at a faster rate for all the values of Td)The solid sphere will cool a faster rate for all the values of TCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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ample number of questions to practice A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the body and thatof the surroundings is T, thena)Both spheres will cool at the same rate for small values of Tb)Both spheres will cool at the same reactor small values of Tc)The hollow sphere will cool at a faster rate for all the values of Td)The solid sphere will cool a faster rate for all the values of TCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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