Radiation of a Spherical Body Inside a Black Body

In summary, the question involves a spherical body with area A and emissivity 0.6 kept inside a perfectly black body. The total heat radiated by the body at temperature T is being asked and four options are given. The Stefan-Boltzmann's Law is used to calculate the power radiated by the body, but the question asks for total heat radiated which may or may not be affected by the black body. The correct answer is D, but the question itself is confusing and may involve the concept of emissivity and absorptivity.
  • #1
erisedk
374
7

Homework Statement


A spherical body of area A and emissivity 0.6 is kept inside a perfectly black body. Total heat radiated by the body at temperature T is
(A) 0.4σAT4
(B) 0.8σAT4
(C) 0.6σAT4
(D) 1.0σAT4

Homework Equations


Stefan-Boltzmann's Law: P = AεσT4

The Attempt at a Solution


If it wasn't inside the black body, the answer would be (C). But it is inside one and I don't know what to do about it. Wouldn't the black body just absorb all the power radiated? We also don't know what temperature the black body is. And the question asks for total heat radiated, not power which is confusing because the answers will have dimensions of power, unless they've just omitted saying total heat per second. Honestly, I've always been a bit confused with emissivity and absorptivity. Please help.
 
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  • #2
I'm as puzzled by the question as you are. Yes, clearly they mean rate of heat emission. I do not interpret total heat as net heat, so do not see how the black body affects it. Maybe that is the point of the question, that it is not affected. If it means the net heat then indeed you would need to know the temperature of the black body.
 
  • #3
The answer is D, if it helps. Otherwise, it seems like a pretty weird question, so I guess I'll skip it.
 

1. What is the concept of radiation of a spherical body inside a black body?

The concept of radiation of a spherical body inside a black body refers to the process by which a spherical body, such as a planet or star, emits and absorbs electromagnetic radiation within a black body, which is an idealized object that absorbs all incoming radiation without reflecting or transmitting any. This process is described by the Stefan-Boltzmann law, which states that the total radiation emitted by a black body is proportional to the fourth power of its absolute temperature.

2. How is the radiation of a spherical body inside a black body related to the temperature of the body?

The radiation of a spherical body inside a black body is directly related to the temperature of the body. According to the Stefan-Boltzmann law, the total radiation emitted by a black body is proportional to the fourth power of its temperature. This means that as the temperature of the body increases, the amount of radiation it emits also increases exponentially.

3. How does the size of a spherical body affect its radiation inside a black body?

The size of a spherical body has a significant effect on its radiation inside a black body. According to the Stefan-Boltzmann law, the total radiation emitted by a black body is proportional to the surface area of the body. Therefore, a larger spherical body will emit more radiation than a smaller one, assuming they have the same temperature.

4. What is the role of emissivity in the radiation of a spherical body inside a black body?

Emissivity is a measure of how well a material or object emits or absorbs radiation. In the context of radiation of a spherical body inside a black body, emissivity plays a critical role in determining the amount of radiation emitted. A higher emissivity means that the body will emit more radiation, while a lower emissivity means that it will emit less. In a black body, emissivity is assumed to be 1, meaning that it absorbs and radiates all incoming radiation.

5. How does the radiation of a spherical body inside a black body affect its temperature?

The radiation of a spherical body inside a black body has a significant impact on its temperature. As the body emits radiation, it loses energy, which causes its temperature to decrease. However, if the body is receiving more radiation than it is emitting, its temperature will increase. The balance between incoming and outgoing radiation determines the equilibrium temperature of the body, which is dependent on factors such as its size, emissivity, and the temperature of the black body it is inside.

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