Heat transfer stefan-Boltzmann

In summary, the conversation is about determining the temperature of a 60 watt lamp's filament using the Stefan-Boltzmann constant and given parameters of the filament's area and absorptivity. The equation used is Q= εσAT^4 and the computed temperature is 4169.894K. However, the answer may have too many significant figures and the units for the Stefan-Boltzmann constant may be incorrect. The correct answer given on the question sheet is 3800K.
  • #1
livstudent
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Homework Statement



Determine the temperature of the filament of a 60watt lamp, if the filament has an area of 10mm^2 and an absorptivity of 0.35. Assume stefan-Boltzmann constant is 5.67*10^-8 W/(m.K^4).

Homework Equations





The Attempt at a Solution



The equation I have attempted with is

Q= εσAT^4

60= 0.35*(5.67*10^-8)*(0.00001m^2)*(T^4)

T^4= 60/(0.35* 5.67*10^-8* 0.00001)

then 4th root of answer = 4169.894

is this correct?
 
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  • #2
Looks correct with the following comments:

Your answer has too many significant figures.
Your units for the Stefan-Boltzmann constant are wrong.
 
  • #3
Thats what I have been given on my question sheet, also they just give numerical answers and on the sheet it says the correct answer is 3800K that is why i put it up to check??
 
  • #4
I compute the same answer as you did.
 
  • #5


I would provide the following response to this content:

Yes, your calculation using the Stefan-Boltzmann equation is correct. The temperature of the filament of the 60 watt lamp would be approximately 4169.89 K. This is a high temperature and is expected for a filament in a light bulb, as it needs to reach high temperatures in order to emit visible light.
 

1. What is the Stefan-Boltzmann law?

The Stefan-Boltzmann law is a physical law that describes the relationship between the temperature and the total amount of thermal radiation emitted by a blackbody. It states that the total energy radiated per unit surface area of a blackbody is proportional to the fourth power of its absolute temperature, and is expressed by the equation P = σεAT⁴, where P is the power radiated, σ is the Stefan-Boltzmann constant, ε is the emissivity of the object, and T is its absolute temperature.

2. How is the Stefan-Boltzmann law related to heat transfer?

The Stefan-Boltzmann law is related to heat transfer because it describes the amount of thermal radiation emitted by an object, which is a form of heat transfer. The law states that the rate of heat transfer through thermal radiation is directly proportional to the fourth power of the temperature difference between two objects.

3. What is the significance of the Stefan-Boltzmann constant?

The Stefan-Boltzmann constant is a fundamental physical constant that relates the amount of radiation emitted by a blackbody to its absolute temperature. It is used in various calculations involving heat transfer and is crucial in understanding the energy balance of objects in the universe.

4. Can the Stefan-Boltzmann law be applied to all objects?

No, the Stefan-Boltzmann law is only applicable to ideal blackbodies, which are theoretical objects that absorb and emit all radiation that falls on them. Real-world objects have different emissivity values, which affect their radiation emission and cannot be accurately described by the Stefan-Boltzmann law.

5. How does the Stefan-Boltzmann law impact climate change?

The Stefan-Boltzmann law plays a crucial role in understanding the Earth's energy balance and its impact on climate change. As the Earth's average temperature increases, the amount of thermal radiation emitted by the Earth also increases according to the Stefan-Boltzmann law. This can contribute to the greenhouse effect and lead to further warming of the Earth's atmosphere.

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