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The intensity of radiation emitted by the sun has its maximum value at a wavelength of 510 nm and that emitted by the North Star has the maximum value at 350 nm. If these stars behave like black bodies, then the ratio of the surface temperatures of the sun and the North Star is
Radiation is the transfer of energy through electromagnetic waves without requiring a medium. It occurs in all objects emitting heat, with hotter bodies radiating more energy. Examples include sunlight warming Earth and heat emitted by a fire. Radiation plays a vital role in energy transfer in space and everyday life.
Class 11 Physics Chapter 10 Thermal Properties of Matter focuses on heat transfer methods like conduction, convection, and radiation. It explains thermal expansion, specific heat capacity, calorimetry, and latent heat. The chapter highlights their practical applications and significance in understanding thermal phenomena observed in nature and various scientific processes.
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We can use Wien’s Law to solve this problem. Wien’s Law relates the temperature of a black body to the wavelength at which it emits maximum radiation. The formula is:
λₘₐₓ T = b
Where:
– λₘₐₓ is the wavelength at which the maximum intensity occurs,
– T is the temperature of the black body,
– b is Wien’s constant, which is approximately 2.898 × 10⁶ nm·K.
Let’s denote the temperatures of the Sun and the North Star as Tₛᵤₙ and Tₙₒᵣₜₕₛₜₐᵣ, and their corresponding maximum wavelengths as λₛᵤₙ and λₙₒᵣₜₕₛₜₐᵣ.
For the Sun:
λₛᵤₙ = 510 nm
For the North Star:
λₙₒᵣₜₕₛₜₐᵣ = 350 nm
Applying Wien’s Law for both stars, we can write:
λₛᵤₙ Tₛᵤₙ = λₙₒᵣₜₕₛₜₐᵣ Tₙₒᵣₜₕₛₜₐᵣ
Now, solving for the ratio of their temperatures:
Tₛᵤₙ / Tₙₒᵣₜₕₛₜₐᵣ = λₙₒᵣₜₕₛₜₐᵣ / λₛᵤₙ
Substituting the values:
Tₛᵤₙ / Tₙₒᵣₜₕₛₜₐᵣ = 350 / 510 ≈ 0.686
Therefore, the ratio of surface temperatures of Sun and North Star is approximately 0.69.
Answer: 0.69
See more:
https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/