Thermodynamics question i dont get

[ice87]

I got this question as part of an assignment. I read the section of the textbook that we were supposed to, and couldn't find anything to help me with, so here goes:

To measure temperatures, physicists and astronomers often use the variation of intensity of electromagnetic radiation emitted by an object. The wavelength at which the intensity is greatest is given by the equation ΛT = 0.2898cm K, where T is the object temperature in Kelvins. In 1965, microwave radiation peaking at Λ = 0.107 was discovered coming in all directions from space. To which temperature does this correspond?

 

[Galileo]

What part do you not understand? The radiation has a certain intensity profile, it radiates light (or photons) more at certain frequencies (or wavelengths) for a given temperature, so the intensity of the radiation is a function of wavelength and temperature.
You have been given that this profile has a single peak, and that the relation between temperature and the wavelength with maximum intensity is $\Lambda T = 0.2898 cmK$ where $\Lambda$ is the wavelength in cm.

 

[ice87]

I don't get what I'm supposed to do. We haven't even had one lecture on this. Am I to give a definite number value for the temperature? I did this : 0.2898cmK/0.107cm and got 2.7K, am I on the right track?

 

[HallsofIvy]

"To which temperature does this correspond?"

Yep, that's pretty much asking for one number! (And a temperature at that!)

You are told that $\Lambda T = 0.2898 cmK$
and you are given that $\Lambda$= 0.107.
(Surely the problem said 0.107 cm?)

Looks to me like 0.107T= 0.2898 cmK so that T= (0.298 cmK)/(0.107 cm) giving an answer in degrees Kelvin. Yes, that's your answer.

(Assuming that $\Lambda$= 0.107 cm. You might want to check that it wasn't really mm or microns or something like that!)