Suppose the sun expands so that its radius becomes 100 times its present radius and its surface temperature becomes half of its present value. The total energy emitted by it then will increase by a factor of
Energy is the capacity to perform work or produce change. It exists in various forms like kinetic, potential, thermal and chemical. Energy can neither be created nor destroyed but only transformed from one form to another, as stated in the law of conservation of energy, making it fundamental to all physical processes.
Class 11 Physics Chapter 10 Thermal Properties of Matter focuses on heat transfer and its effects on materials. It explains conduction convection and radiation, thermal expansion of solids liquids and gases, specific heat capacity, calorimetry, Newton’s law of cooling and the Stefan-Boltzmann law. These concepts are crucial for understanding thermal phenomena in daily life.
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We can apply the Stefan-Boltzmann law to compute the change in the total energy emitted:
E = σ T⁴ A
Here,
– E is the total energy emitted
– σ is the Stefan-Boltzmann constant
– T is the surface temperature
– A is the surface area of the object
Surface area of sphere is given as:
A = 4π r²
If the radius of the sun increases by a factor of 100 and the temperature decreases by half, we need to calculate the change in energy.
Let the initial energy be E₁, and the final energy be E₂.
Initial energy: E₁ = σ T₁⁴ (4π r₁²)
Final energy: E₂ = σ (T₁/2)⁴ (4π (100r₁)²)
Simplifying the ratio of the final energy to the initial energy:
(E₂ / E₁) = (T₁/2)⁴ (100²) = (1/16) (10000) = 625
Thus, the total energy emitted increases by a factor of 625.
The correct answer is 625.
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