Solve Thermal Radiation HW: Find Temperature Inside Insulating Case

In summary, the problem involves an iPod running inside a 2.5mm thick insulating case with a thermal conductivity of 0.02W/K/m. The case is black and at 25 degrees C, while the surroundings are at 20 degrees C, with energy exchange occurring through radiation. The task is to determine the temperature inside the case, taking into account the effects of radiation. The thermal diffusion equation may not be applicable in this case.
  • #1
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Homework Statement



An ipod is left running inside a thin insulating case 2.5mm thick with thermal conductivity of 0.02W/K/m. The case is black and at 25 degrees C and exchanges energy with its surroundings, all of which are at 20 degrees C by radiation alone. What is the temperature inside the case?


Homework Equations





The Attempt at a Solution



Not sure how to do this?

Am i right that we don't use the thermal diffusion equation because it says "by radiation alone"..

Not sure how to do it, especially as we don't know the shape of the case etc..?

Help please! :)
 
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  • #2
I believe the radiation heat transfer limitation only applies between the case and the air.
 

1. How do you calculate thermal radiation?

Thermal radiation can be calculated using the Stefan-Boltzmann law, which states that the power emitted by an object is proportional to the fourth power of its temperature. This can be expressed as P = σεAT^4, where P is the power emitted, σ is the Stefan-Boltzmann constant, ε is the emissivity of the object, A is its surface area, and T is its temperature in Kelvin.

2. What factors affect thermal radiation?

The amount of thermal radiation emitted by an object is affected by several factors, including its temperature, surface area, and emissivity. Additionally, the type of material the object is made of can also impact its thermal radiation properties.

3. How does insulation affect thermal radiation?

Insulation can reduce the amount of thermal radiation emitted by an object by trapping the heat within its structure. This is due to the insulating material's low emissivity, which prevents heat from escaping through radiation. Insulation can also prevent outside sources of thermal radiation from affecting the temperature inside an object.

4. What is the difference between thermal radiation and conduction/convection?

Thermal radiation is the transfer of heat through electromagnetic waves, while conduction and convection are both forms of heat transfer through physical contact. Conduction involves heat transfer through a solid material, while convection is the transfer of heat through a fluid medium.

5. How do you find the temperature inside an insulating case?

To find the temperature inside an insulating case, you can use the Stefan-Boltzmann law and the properties of the insulating material to calculate the amount of thermal radiation being emitted and absorbed. You can also consider the effects of conduction and convection on the temperature inside the case. Using these factors, you can determine the equilibrium temperature inside the insulating case.

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