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If the temperature difference between the body and surrounding is small, then the rate of loss of heat is directly proportional to
- a)Temperature of two bodies
- b)Nature of two bodies
- c)Pressure difference of the body
- d)Size of the two bodies
Correct answer is option 'A'. Can you explain this answer?
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If the temperature difference between the body and surrounding is smal...
The rate of loss of heat by a body is directly proportional to its excess temperature over that of the surroundings provided that this excess is small.
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If the temperature difference between the body and surrounding is smal...
Where are the two bodies and rate of loss of heat also depends on sigma( property of material)
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If the temperature difference between the body and surrounding is smal...
Understanding the Stefan-Boltzmann Law
The Stefan-Boltzmann law describes how a perfect black body radiates energy. According to this law, the total energy radiated per unit area of a black body is directly proportional to the fourth power of its absolute temperature (T). This relationship can be expressed mathematically as:
Equation:
\[ E = \sigma T^4 \]
Where:
- **E** = Total energy radiated per unit area
- **σ** = Stefan-Boltzmann constant (approximately \(5.67 \times 10^{-8} \, W/m^2K^4\))
- **T** = Absolute temperature in Kelvin
Proportionality to Temperature
According to the law:
- The rate of energy radiation increases significantly with temperature.
- If the temperature doubles, the energy radiated increases by a factor of \(2^4 = 16\).
Physical Interpretation
- The fourth power dependency means that even small increases in temperature can result in large increases in emitted energy.
- For example, if a radiator's temperature rises from 300 K to 400 K, the energy emitted increases from \(300^4\) to \(400^4\), demonstrating the dramatic effect of temperature on thermal radiation.
Applications of the Law
- The Stefan-Boltzmann law is essential in fields such as astrophysics, climate science, and engineering.
- It helps in understanding stellar luminosity, the heating of planets, and the efficiency of thermal systems.
In summary, the Stefan-Boltzmann law emphasizes that the radiant energy per unit area of a perfect radiator is proportional to the fourth power of its temperature, making option 'D' the correct choice.
The Stefan-Boltzmann law describes how a perfect black body radiates energy. According to this law, the total energy radiated per unit area of a black body is directly proportional to the fourth power of its absolute temperature (T). This relationship can be expressed mathematically as:
Equation:
\[ E = \sigma T^4 \]
Where:
- **E** = Total energy radiated per unit area
- **σ** = Stefan-Boltzmann constant (approximately \(5.67 \times 10^{-8} \, W/m^2K^4\))
- **T** = Absolute temperature in Kelvin
Proportionality to Temperature
According to the law:
- The rate of energy radiation increases significantly with temperature.
- If the temperature doubles, the energy radiated increases by a factor of \(2^4 = 16\).
Physical Interpretation
- The fourth power dependency means that even small increases in temperature can result in large increases in emitted energy.
- For example, if a radiator's temperature rises from 300 K to 400 K, the energy emitted increases from \(300^4\) to \(400^4\), demonstrating the dramatic effect of temperature on thermal radiation.
Applications of the Law
- The Stefan-Boltzmann law is essential in fields such as astrophysics, climate science, and engineering.
- It helps in understanding stellar luminosity, the heating of planets, and the efficiency of thermal systems.
In summary, the Stefan-Boltzmann law emphasizes that the radiant energy per unit area of a perfect radiator is proportional to the fourth power of its temperature, making option 'D' the correct choice.
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If the temperature difference between the body and surrounding is small, then the rate of loss of heat is directly proportional toa)Temperature of two bodiesb)Nature of two bodiesc)Pressure difference of the bodyd)Size of the two bodiesCorrect answer is option 'A'. Can you explain this answer?
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