Mechanical Engineering Exam > Mechanical Engineering Questions > Two spheres A and B of same material have rad...
Start Learning for Free
Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is:
- a)Greater than that of sphere B
- b)Less than that of sphere B
- c)Equal to that of sphere B
- d)Equal to double that of sphere B
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two spheres A and B of same material have radii 1 m and 4 m and temper...
Ans. (c)
Most Upvoted Answer
Two spheres A and B of same material have radii 1 m and 4 m and temper...
Understanding Blackbody Radiation
The energy radiated by a blackbody is described by the Stefan-Boltzmann Law, which states that the total energy radiated per unit surface area is proportional to the fourth power of its absolute temperature.
Stefan-Boltzmann Law
- The formula is given by:
E = σT^4
where E is the energy radiated per unit area, σ is the Stefan-Boltzmann constant, and T is the absolute temperature in Kelvin.
Calculating Energy for Sphere A and B
- Sphere A:
- Radius = 1 m
- Temperature = 4000 K
- Surface Area = 4π(1^2) = 4π m²
- Energy radiated (EA) = σ(4000^4) * 4π
- Sphere B:
- Radius = 4 m
- Temperature = 2000 K
- Surface Area = 4π(4^2) = 64π m²
- Energy radiated (EB) = σ(2000^4) * 64π
Comparing Energy Radiated
- Calculating EA and EB:
- EA = σ * 4π * (4000^4)
- EB = σ * 64π * (2000^4)
- Simplifying the comparison:
- 4000^4 = 256 * 1000^4
- 2000^4 = 16 * 1000^4
- Thus, EB becomes 64π * (16 * 1000^4) = 1024π * σ
- Final Comparison:
- EA = 1024π * σ
- EB = 1024π * σ
Conclusion
Both spheres radiate equal energy despite their different sizes and temperatures, hence the correct answer is option C: Equal to that of sphere B.
The energy radiated by a blackbody is described by the Stefan-Boltzmann Law, which states that the total energy radiated per unit surface area is proportional to the fourth power of its absolute temperature.
Stefan-Boltzmann Law
- The formula is given by:
E = σT^4
where E is the energy radiated per unit area, σ is the Stefan-Boltzmann constant, and T is the absolute temperature in Kelvin.
Calculating Energy for Sphere A and B
- Sphere A:
- Radius = 1 m
- Temperature = 4000 K
- Surface Area = 4π(1^2) = 4π m²
- Energy radiated (EA) = σ(4000^4) * 4π
- Sphere B:
- Radius = 4 m
- Temperature = 2000 K
- Surface Area = 4π(4^2) = 64π m²
- Energy radiated (EB) = σ(2000^4) * 64π
Comparing Energy Radiated
- Calculating EA and EB:
- EA = σ * 4π * (4000^4)
- EB = σ * 64π * (2000^4)
- Simplifying the comparison:
- 4000^4 = 256 * 1000^4
- 2000^4 = 16 * 1000^4
- Thus, EB becomes 64π * (16 * 1000^4) = 1024π * σ
- Final Comparison:
- EA = 1024π * σ
- EB = 1024π * σ
Conclusion
Both spheres radiate equal energy despite their different sizes and temperatures, hence the correct answer is option C: Equal to that of sphere B.
|
Explore Courses for Mechanical Engineering exam
|
|
Top Courses for Mechanical EngineeringView all
Question Description
Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer?.
Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is: a)Greater than that of sphere Bb)Less than that of sphere Bc)Equal to that of sphere Bd)Equal to double that of sphere BCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily