A Conceptual doubt in a problem on Wien's Law

[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.

 

[Doc Al]

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.

 

[DrClaude]

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."

 

[Doc Al]

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.

 

[DrClaude]

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.

 

[Doc Al]

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.

 

[DrClaude]

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.

 

[Doc Al]

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!

 

[warhammer]

@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.

 

[DrClaude]

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.

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.