# A Conceptual doubt in a problem on Wien's Law

• warhammer
In summary, the given wavelength of 700nm is used as the peak wavelength in Wien's law to find the temperature to be 4140K. However, it is stated that this wavelength is a maximum and there is confusion between options (a) and (d) for the correct temperature. It is determined that the temperature must be less than 4140K due to the iron being in its solid form and the color of the iron's glow not necessarily corresponding to the peak wavelength of the energy per unit area. This can be answered without knowing the melting point of the material being heated.
warhammer
Homework Statement
A blacksmith puts an iron rod in a furnace and takes it out when it starts glowing red. Assume the wavelength of the red light emitted by the rod to be 700 nm. The temperature of the rod should be (Wien’s constant = 2.898 x 10-3 m.K):
(a) 4140 K
(b) <4140 K
(c) >4140 K
(d) In the range 4140 K-4240 K
Relevant Equations
Wien's Displacement Law- λT=2.898*10^-3
Given λ=700nm, we use the equation mentioned above and find the Temperature to be 4140K. However, my doubt is that the wavelength specified to be used above is a maximum and I'm not sure if the answer is (a) or (d) considering that the latter is a range of the temperature.

warhammer said:
However, my doubt is that the wavelength specified to be used above is a maximum
You are to use the given wavelength as the peak wavelength. Wien's law will then give you the temperature.

Doc Al said:
You are to use the given wavelength as the peak wavelength.
I'm not sure that this is correct. It's not compatible with how I interpret "takes it out when it starts glowing red."

DrClaude said:
I'm not sure that this is correct. It's not compatible with how I interpret "takes it out when it starts glowing red."
You may be right. I found the statement rather vague, so I interpreted it to mean that the peak wavelength was what was meant.

Doc Al said:
You may be right. I found the statement rather vague, so I interpreted it to mean that the peak wavelength was what was meant.
I think that the presence of lower/upper bounds in the possible answers is another clue that plugging the wavelength in Wien's displacement law is not sufficient.

DrClaude said:
I think that the presence of lower/upper bounds in the possible answers is another clue that plugging the wavelength in Wien's displacement law is not sufficient.
I thought the opposite. What information is available to give a range of temperatures? Also answers c and d would overlap.

Doc Al said:
I thought the opposite. What information is available to give a range of temperatures? Also answers c and d would overlap.
I'll explain later, after @warhammer has had time to work the problem.

I think you have to think about all that is happening, not just plug-and-play with the equation.

warhammer and Doc Al
DrClaude said:
I think you have to think about all that is happening, not just plug-and-play with the equation.
On further thought, I'd say you are correct. Thanks!

@DrClaude @Doc Al Apologies for the late response. I seemed to figure it out. The temperature should be less than 4140K (Option b) because logically thinking the iron wouldn't be in its current solid form if the temp were really that high! (and this is a fairly regular job for the blacksmiths). If we use Wien's Law, the wavelength is supposed to be maximum and the energy is supposed to be maximum as well. Seeing red color doesn't imply that the energy per unit area peak is somewhere around the specified wavelength per se the Planck's Blackbody distribution law. Thus the temperature is supposed to be less than 4140K.

warhammer said:
The temperature should be less than 4140K (Option b) because logically thinking the iron wouldn't be in its current solid form if the temp were really that high!
You should be able to answer the question without knowing the melting point of the material being heated.

warhammer said:
Seeing red color doesn't imply that the energy per unit area peak is somewhere around the specified wavelength per se the Planck's Blackbody distribution law. Thus the temperature is supposed to be less than 4140K.
That's it. If the iron is just starting to glow at 700 nm, then the peak wavelength must still be in the infra-red, so T < 4140 K.

## 1. What is Wien's Law?

Wien's Law, also known as the displacement law, is a relationship between temperature and the peak wavelength of blackbody radiation. It states that the peak wavelength is inversely proportional to the temperature, meaning that as temperature increases, the peak wavelength decreases.

## 2. How is Wien's Law used in scientific research?

Wien's Law is commonly used in astrophysics and cosmology to determine the temperature of stars and other celestial objects. It is also used in materials science to study the thermal properties of various materials and in the development of infrared technology.

## 3. What is a conceptual doubt in a problem on Wien's Law?

A conceptual doubt in a problem on Wien's Law refers to a question or confusion about the underlying principles and concepts related to the law, rather than a specific numerical calculation or application.

## 4. How can I overcome a conceptual doubt in a problem on Wien's Law?

To overcome a conceptual doubt, it is important to first review the basic principles of Wien's Law and make sure you understand how it is applied. You can also consult with other scientists or experts in the field for clarification or additional resources.

## 5. Can Wien's Law be applied to all types of radiation?

No, Wien's Law is specifically applicable to blackbody radiation, which is the thermal radiation emitted by an object at a given temperature. Other types of radiation, such as synchrotron radiation or Cherenkov radiation, follow different laws and principles.

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