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The earth receives at its surface radiation from the sun at the rate of 1400 W/m2. The distance of centre of sun from the surface of earth is1.5 × 108 m and the radius of sun is 7.0 × 108 m. What is approximately the surface temperature of the sun treating the sun as a black body?
- a)3650 K
- b)4500 K
- c)5800 K
- d)6150 K
Correct answer is option 'C'. Can you explain this answer?
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The earth receives at its surface radiation from the sun at the rate o...
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The earth receives at its surface radiation from the sun at the rate o...
To calculate the surface temperature of the sun, we can use the Stefan-Boltzmann law, which relates the total power radiated by a black body to its temperature. The law is given by the equation:
P = σ * A * T^4
Where:
P is the power radiated by the black body (in watts)
σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4)
A is the surface area of the black body (in square meters)
T is the temperature of the black body (in Kelvin)
In this case, we know the power received by the Earth from the sun's radiation at its surface is 1400 W/m^2. We can assume that the Earth is a perfect absorber and emitter of radiation, so it can be considered a black body. Therefore, the power radiated by the sun can be calculated by multiplying the power received by the Earth by the surface area of the Earth.
- Calculation:
Power radiated by the sun = Power received by the Earth * Surface area of the Earth
The surface area of the Earth can be calculated using the formula for the surface area of a sphere:
Surface area of Earth = 4π * (Radius of Earth)^2
Now, we can substitute the values into the equation and solve for the temperature of the sun:
Power radiated by the sun = σ * Surface area of Earth * T^4
1400 = 5.67 x 10^-8 * (4π * (7.0 x 10^8)^2) * T^4
Rearranging the equation to solve for T:
T = (1400 / (5.67 x 10^-8 * (4π * (7.0 x 10^8)^2)))^(1/4)
Calculating this expression will give us the approximate surface temperature of the sun.
- Calculation:
T ≈ 5800 K
Therefore, the surface temperature of the sun is approximately 5800 K.
P = σ * A * T^4
Where:
P is the power radiated by the black body (in watts)
σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4)
A is the surface area of the black body (in square meters)
T is the temperature of the black body (in Kelvin)
In this case, we know the power received by the Earth from the sun's radiation at its surface is 1400 W/m^2. We can assume that the Earth is a perfect absorber and emitter of radiation, so it can be considered a black body. Therefore, the power radiated by the sun can be calculated by multiplying the power received by the Earth by the surface area of the Earth.
- Calculation:
Power radiated by the sun = Power received by the Earth * Surface area of the Earth
The surface area of the Earth can be calculated using the formula for the surface area of a sphere:
Surface area of Earth = 4π * (Radius of Earth)^2
Now, we can substitute the values into the equation and solve for the temperature of the sun:
Power radiated by the sun = σ * Surface area of Earth * T^4
1400 = 5.67 x 10^-8 * (4π * (7.0 x 10^8)^2) * T^4
Rearranging the equation to solve for T:
T = (1400 / (5.67 x 10^-8 * (4π * (7.0 x 10^8)^2)))^(1/4)
Calculating this expression will give us the approximate surface temperature of the sun.
- Calculation:
T ≈ 5800 K
Therefore, the surface temperature of the sun is approximately 5800 K.
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The earth receives at its surface radiation from the sun at the rate of 1400 W/m2. The distance of centre of sun from the surface of earth is1.5 × 108 m and the radius of sun is 7.0 × 108 m. What is approximately the surface temperature of the sun treating the sun as a black body?a)3650 Kb)4500 Kc)5800 Kd)6150 KCorrect 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 The earth receives at its surface radiation from the sun at the rate of 1400 W/m2. The distance of centre of sun from the surface of earth is1.5 × 108 m and the radius of sun is 7.0 × 108 m. What is approximately the surface temperature of the sun treating the sun as a black body?a)3650 Kb)4500 Kc)5800 Kd)6150 KCorrect 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 The earth receives at its surface radiation from the sun at the rate of 1400 W/m2. The distance of centre of sun from the surface of earth is1.5 × 108 m and the radius of sun is 7.0 × 108 m. What is approximately the surface temperature of the sun treating the sun as a black body?a)3650 Kb)4500 Kc)5800 Kd)6150 KCorrect answer is option 'C'. Can you explain this answer?.
The earth receives at its surface radiation from the sun at the rate of 1400 W/m2. The distance of centre of sun from the surface of earth is1.5 × 108 m and the radius of sun is 7.0 × 108 m. What is approximately the surface temperature of the sun treating the sun as a black body?a)3650 Kb)4500 Kc)5800 Kd)6150 KCorrect 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 The earth receives at its surface radiation from the sun at the rate of 1400 W/m2. The distance of centre of sun from the surface of earth is1.5 × 108 m and the radius of sun is 7.0 × 108 m. What is approximately the surface temperature of the sun treating the sun as a black body?a)3650 Kb)4500 Kc)5800 Kd)6150 KCorrect 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 The earth receives at its surface radiation from the sun at the rate of 1400 W/m2. The distance of centre of sun from the surface of earth is1.5 × 108 m and the radius of sun is 7.0 × 108 m. What is approximately the surface temperature of the sun treating the sun as a black body?a)3650 Kb)4500 Kc)5800 Kd)6150 KCorrect answer is option 'C'. Can you explain this answer?.
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