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If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of [1993]
- a)2
- b)4
- c)8
- d)16
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If the temperature of the sun is doubled, the rate of energy received ...
Amount of energy radiated ∝ T4
Most Upvoted Answer
If the temperature of the sun is doubled, the rate of energy received ...
As energy depends on temperature raised to the power 4..
so 2 to the power 4..i.e. 16 times.
so 2 to the power 4..i.e. 16 times.
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Community Answer
If the temperature of the sun is doubled, the rate of energy received ...
To understand why the rate of energy received on Earth would be increased by a factor of 16 if the temperature of the sun is doubled, we need to consider the relationship between temperature and energy radiated by a black body.
1. Stefan-Boltzmann Law:
The energy radiated by a black body is proportional to the fourth power of its temperature. This relationship is described by the Stefan-Boltzmann Law, which states that the power radiated per unit area (P) is given by the equation P = σT^4, where σ is the Stefan-Boltzmann constant.
2. Doubling the Temperature:
If the temperature of the sun is doubled, let's say from T1 to T2, we can write the equation for the power radiated per unit area as P2 = σT2^4.
3. Relationship between Powers:
To find the factor by which the rate of energy received on Earth is increased, we need to compare the powers before and after doubling the temperature. Let's call the initial power P1.
P1 = σT1^4
P2 = σT2^4
4. Ratio of Powers:
Now, let's calculate the ratio of the two powers:
P2/P1 = (σT2^4) / (σT1^4)
= (T2^4) / (T1^4)
5. Doubling the Temperature:
Since we are doubling the temperature, we have T2 = 2T1.
P2/P1 = (2T1)^4 / T1^4
= 16(T1^4) / (T1^4)
= 16
6. Conclusion:
The ratio of the powers is 16, which means that if the temperature of the sun is doubled, the rate of energy received on Earth will be increased by a factor of 16. Therefore, the correct answer is option D) 16.
1. Stefan-Boltzmann Law:
The energy radiated by a black body is proportional to the fourth power of its temperature. This relationship is described by the Stefan-Boltzmann Law, which states that the power radiated per unit area (P) is given by the equation P = σT^4, where σ is the Stefan-Boltzmann constant.
2. Doubling the Temperature:
If the temperature of the sun is doubled, let's say from T1 to T2, we can write the equation for the power radiated per unit area as P2 = σT2^4.
3. Relationship between Powers:
To find the factor by which the rate of energy received on Earth is increased, we need to compare the powers before and after doubling the temperature. Let's call the initial power P1.
P1 = σT1^4
P2 = σT2^4
4. Ratio of Powers:
Now, let's calculate the ratio of the two powers:
P2/P1 = (σT2^4) / (σT1^4)
= (T2^4) / (T1^4)
5. Doubling the Temperature:
Since we are doubling the temperature, we have T2 = 2T1.
P2/P1 = (2T1)^4 / T1^4
= 16(T1^4) / (T1^4)
= 16
6. Conclusion:
The ratio of the powers is 16, which means that if the temperature of the sun is doubled, the rate of energy received on Earth will be increased by a factor of 16. Therefore, the correct answer is option D) 16.
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If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of [1993]a)2b)4c)8d)16Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of [1993]a)2b)4c)8d)16Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of [1993]a)2b)4c)8d)16Correct answer is option 'D'. Can you explain this answer?.
If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of [1993]a)2b)4c)8d)16Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of [1993]a)2b)4c)8d)16Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of [1993]a)2b)4c)8d)16Correct answer is option 'D'. Can you explain this answer?.
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