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Assertion (A): Heat transfer at high temperature is dominated byradiation rather than convection.
Reason (R): Radiation depends on fourth power of temperature while convection depends on unit power relationship.
- a)Both A and R are individually true and R is the correct explanation of A
- b)Both A and R are individually true but R is not the of A
- c)A is true but R is false
- d)A is false but R is true
Correct answer is option 'A'. Can you explain this answer?
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Assertion (A): Heat transfer at high temperature is dominated byradiat...
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Assertion (A): Heat transfer at high temperature is dominated byradiat...
Heat transfer can occur through different mechanisms such as conduction, convection, and radiation. In the case of high temperatures, radiation becomes the dominant mode of heat transfer.
Assertion (A): Heat transfer at high temperature is dominated by radiation rather than convection.
Reason (R): Radiation depends on the fourth power of temperature, while convection depends on a linear relationship.
Let's analyze each statement individually:
Statement (A): Heat transfer at high temperature is dominated by radiation rather than convection.
This statement is true. At high temperatures, the heat transfer by radiation becomes more significant compared to convection. Radiation is the transfer of heat through electromagnetic waves, which do not require any medium for propagation. It can occur in vacuum and is not dependent on the presence of a material medium. Therefore, radiation can be the primary mode of heat transfer in high-temperature environments where the medium may be scarce or non-existent.
Statement (R): Radiation depends on the fourth power of temperature, while convection depends on a linear relationship.
This statement is also true. According to Stefan-Boltzmann's law, the rate of heat transfer by radiation is directly proportional to the fourth power of the absolute temperature. The equation is given by:
Q = σ * ε * A * (T₁⁴ - T₂⁴)
where Q is the rate of heat transfer, σ is the Stefan-Boltzmann constant, ε is the emissivity of the surface, A is the surface area, and T₁ and T₂ are the temperatures of the two bodies.
On the other hand, convection is the transfer of heat through the movement of fluids. It depends on the temperature difference between the surface and the fluid and is usually described by Newton's law of cooling:
Q = h * A * (T - Tₒ)
where Q is the rate of heat transfer, h is the convective heat transfer coefficient, A is the surface area, T is the surface temperature, and Tₒ is the temperature of the fluid.
The key difference is that the rate of heat transfer by radiation depends on the fourth power of temperature, while convection depends on a linear relationship between temperature and heat transfer rate.
Explanation:
From the above analysis, we can conclude that both statement (A) and statement (R) are individually true, and statement (R) is the correct explanation of statement (A). The dominance of radiation at high temperatures is due to its dependence on the fourth power of temperature, which leads to a significant increase in heat transfer rate compared to convection.
Assertion (A): Heat transfer at high temperature is dominated by radiation rather than convection.
Reason (R): Radiation depends on the fourth power of temperature, while convection depends on a linear relationship.
Let's analyze each statement individually:
Statement (A): Heat transfer at high temperature is dominated by radiation rather than convection.
This statement is true. At high temperatures, the heat transfer by radiation becomes more significant compared to convection. Radiation is the transfer of heat through electromagnetic waves, which do not require any medium for propagation. It can occur in vacuum and is not dependent on the presence of a material medium. Therefore, radiation can be the primary mode of heat transfer in high-temperature environments where the medium may be scarce or non-existent.
Statement (R): Radiation depends on the fourth power of temperature, while convection depends on a linear relationship.
This statement is also true. According to Stefan-Boltzmann's law, the rate of heat transfer by radiation is directly proportional to the fourth power of the absolute temperature. The equation is given by:
Q = σ * ε * A * (T₁⁴ - T₂⁴)
where Q is the rate of heat transfer, σ is the Stefan-Boltzmann constant, ε is the emissivity of the surface, A is the surface area, and T₁ and T₂ are the temperatures of the two bodies.
On the other hand, convection is the transfer of heat through the movement of fluids. It depends on the temperature difference between the surface and the fluid and is usually described by Newton's law of cooling:
Q = h * A * (T - Tₒ)
where Q is the rate of heat transfer, h is the convective heat transfer coefficient, A is the surface area, T is the surface temperature, and Tₒ is the temperature of the fluid.
The key difference is that the rate of heat transfer by radiation depends on the fourth power of temperature, while convection depends on a linear relationship between temperature and heat transfer rate.
Explanation:
From the above analysis, we can conclude that both statement (A) and statement (R) are individually true, and statement (R) is the correct explanation of statement (A). The dominance of radiation at high temperatures is due to its dependence on the fourth power of temperature, which leads to a significant increase in heat transfer rate compared to convection.
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Assertion (A): Heat transfer at high temperature is dominated byradiation rather than convection.Reason (R): Radiation depends on fourth power of temperature while convection depends on unit power relationship.a)Both A and R are individually true and R is the correct explanation of Ab)Both A and R are individually true but R is not the of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer?
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