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A metal rod at a temperature of 150°C, radiates energy at a rate of 20W. If its temperature is increased to 300°C, then it will radiate at the rate of
Radiation is the emission and transfer of energy through electromagnetic waves or particles. It does not require a medium and can travel through a vacuum. Examples include sunlight, infrared heat and X-rays. Radiation is crucial in processes like energy transfer, climate dynamics and various technological applications.
Class 11 Physics Chapter 10 Thermal Properties of Matter focuses on temperature heat and specific heat capacity. It explains thermal expansion and calorimetry. The chapter also covers heat transfer by conduction and convection and introduces the laws of thermodynamics and the behavior of gases under different temperature and pressure conditions.
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To overcome this problem, we make use of the Stefan-Boltzmann law: that states that power radiated by any body is directly proportional to the fourth power of the absolute temperature as,
P = σ A T⁴
P = the radiated power.
σ is known as Stefan- Boltzmann constant,
A is surface area of body, and
T is temperature in Kelvin.
Since the surface area and the Stefan-Boltzmann constant do not change, we can compare the two powers at two different temperatures by using the ratio of their temperatures raised to the fourth power:
P₂ / P₁ = (T₂ / T₁)⁴
We are given:
– The initial temperature is T₁ = 150°C = 150 + 273 = 423 K
– The final temperature is T₂ = 300°C = 300 + 273 = 573 K
– The initial power is P₁ = 20 W
Applying the formula:
P₂ / 20 = (573 / 423)⁴
Now we can calculate P₂:
P₂ = 20 × (573 / 423)⁴ ≈ 67.34 W
Thus, the power radiated by the metal rod at 300°C will be approximately 67.34 W. The closest answer is: 68.3 W
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