Thermal Radiation Homework: Ranking Objects of Same Material

In summary, considering a cube, sphere, and hemisphere made of the same material at a temperature of 350K in a 300K environment, the objects would rank in order of surface area from greatest to least. This is because the objects will exchange thermal radiation with the environment according to their surface area, and the formula used to calculate this is E=A \sigma T^4 (Stefan's law of black body radiation).
  • #1
tjr39
12
0

Homework Statement



Consider the following three solid object all made of the same material;
1) Cube of edge length r
2) Sphere of radius r
3) Hemisphere of radius r

All object are maintained at a temperature 350K in an envorinment at temperature 300K. Rank the objects according to the net rate at which they exchange thermal radiation with the environment. Justify for full marks.

Homework Equations





The Attempt at a Solution



Im not sure whether to list them simply in order of surface area or not? Is there something else I should be considering? Cheers.
 
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  • #2
tjr39 said:
Im not sure whether to list them simply in order of surface area or not? Is there something else I should be considering? Cheers.

So if you list them in terms of surface area, why would you justify it to be in that order?

Even though you have the correct idea, you should know this formula [itex]E=A \sigma T^4[/itex] (Stefan's law of black body radiation)
 
  • #3


I would approach this problem by considering the Stefan-Boltzmann law, which states that the rate of thermal radiation emitted or absorbed by an object is proportional to the fourth power of its absolute temperature and its surface area. This means that the larger the surface area and the higher the temperature, the greater the rate of thermal radiation exchange.

Based on this law, I would rank the objects in the following order:

1) Hemisphere of radius r
2) Sphere of radius r
3) Cube of edge length r

The hemisphere has the largest surface area out of the three objects, followed by the sphere and then the cube. Additionally, since all objects are at the same temperature, the hemisphere would have the highest rate of thermal radiation exchange with the environment.

Furthermore, I would also consider the shape of the objects. The sphere and hemisphere have curvatures that allow for more efficient thermal radiation exchange compared to the cube, which has flat surfaces. This also contributes to the ranking above.

In conclusion, the ranking of the objects according to the net rate of thermal radiation exchange with the environment would be in the order of hemisphere, sphere, and cube. This is due to the combination of their surface area, temperature, and shape.
 

1. What is thermal radiation?

Thermal radiation is the emission of electromagnetic waves from an object due to its temperature. It is a form of heat transfer that does not require a medium and can travel through a vacuum.

2. How does thermal radiation work?

Thermal radiation occurs when the molecules of an object vibrate due to their temperature. This vibration causes the emission of electromagnetic waves, which carry energy away from the object and transfer it to cooler objects.

3. What is the significance of ranking objects of the same material in thermal radiation?

Ranking objects of the same material in thermal radiation can help us understand how efficiently an object can emit and absorb thermal radiation. This information is useful in various applications, such as designing efficient heating and cooling systems.

4. What factors affect the thermal radiation of an object?

The thermal radiation of an object is affected by its temperature, surface area, and emissivity. Objects with higher temperatures, larger surface areas, and higher emissivity will emit and absorb more thermal radiation than objects with lower values for these factors.

5. How can we rank objects of the same material in terms of thermal radiation?

Objects of the same material can be ranked in terms of thermal radiation by calculating their Stefan-Boltzmann constant, which is a measure of their efficiency in emitting and absorbing thermal radiation. The higher the constant, the more efficient the object is in thermal radiation.

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