# Manipulating λmax * T formula to relate T1 to ∆T

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1. Jun 1, 2015

### Eli Hurley

1. The problem statement, all variables and given/known data
In an experiment to study a black body radiator, the intensity of emitted radiation is measured as a function of the wavelength of the radiation. At a particular temperature T1 the wavelength of the highest intensity radiation is determined to be λ1. When the temperature is changed by ∆T the wavelength of the highest intensity radiation changes to λ2, with λ2 = 0.9λ1. The relationship between T1 and ∆T is:

A. not possible to determine because of the ultra-violet catastrophe.
B. T1 = 9∆T Kelvin
C. T1 = 10/9∆T Kelvin
D. T1 = 0.111∆T Kelvin
E. None of the above

2. Relevant equations
λmax * T = 2.898 10^-3 m * K

3. The attempt at a solution
Since (2.898 10^-3 m * K) is a constant, I immediately discount that in my workings (I can see in the possible answers that it's also not needed).

We know that:

T1 = λ1 and λ2 = 0.9 * λ1

We also know that:

T1 * ∆T = λ2 therefore T1 * ∆T = 0.9 * λ1
^(is this a correct representation?)
I don't think it is, which is why I've changed it to:

T1 * (T2-T1) = λ2 therefore T1 * (T2-T1) = 0.9 * λ1

Upon expansion:

T21 - T11 = λ2 therefore T21 -T11 = 0.9 * λ1

I've been trying to keep my calculations limited to the variables in the possible answers but can't help ending up with T2 (or get rid of the λ1). Is there any other way to manipulate ∆T? My calcs are getting bigger than Ben Hurr and I'm beginning to doubt the legitimacy of the manipulations...

I'm sure this question has to be easier than the lengths I've gone to, if someone can please point out where I've taken a wrong turn that would be greatly appreciated!

2. Jun 1, 2015

### rude man

Oh no, we don't know that. We can't equate a wavelength with a temperature.
You have λ2 = 0.9λ1
T2 = T1 + ∆T
T1 λ1 = T2 λ2.
Work carefully with these , eliminate T2 and you will get the right answer.