For a black body at temperature of 727°C, its radiating power is 60 W and temperature of surroundings is 227°C, then its radiating power will be
Radiating power refers to the amount of energy emitted by a body per unit area per unit time due to its temperature. It is governed by Stefan-Boltzmann law and depends on the body’s temperature and surface properties. A hotter object radiates more energy compared to a cooler one.
Class 11 Physics Chapter 10 Thermal Properties of Matter discusses temperature and heat expansion of solids liquids and gases specific heat capacity latent heat and thermal conductivity. It covers thermal equilibrium laws of thermodynamics and methods of heat transfer including conduction convection and radiation. The chapter also explores the behavior of matter under different thermal conditions.
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To determine the radiating power of a black body according to the Stefan-Boltzmann law:
P = σ A (T⁴ – Tₛ⁴)
Where,
– P is the radiating power
– σ is the Stefan-Boltzmann constant.
– A is the surface area.
– T is the temperature of the body.
– Tₛ is the temperature of the surroundings.
Given:
The temperature of the black body, T = 727°C = 727 + 273 = 1000 K,
– Temperature of environment, Tᵣ = 227°C = 227 + 273 = 500 K,
Radiation intensity at 727°C is 60 W.
The change in radiation power at 727°C is as follows using power ratio due to temperature difference as follows:
(P₂ / P₁) = (T₂ / T₁)⁴
Substitute values:
(P₂ / 60) = (1000 / 500)⁴
(P₂ / 60) = 16
P₂ = 60 × 16 = 960 W
So the correct value for the new radiating power is 240 W.
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