Question

By what factor does the peak frequency change if the celsius temperature of an object is doubled from 20.0 ∘c to 40.0 ∘c?

Answer 1

Answer:

it increases by a factor 1.07

Explanation:

The peak wavelength of an object is given by Wien's displacement law:

$\lambda=\frac{b}{T}$ (1)

where

b is the Wien's displacement constant

T is the temperature (in Kelvins) of the object

given the relationship between frequency and wavelength of an electromagnetic wave:

$f=\frac{c}{\lambda}$

where c is the speed of light, we can rewrite (1) as

$\frac{c}{f}=\frac{b}{T}\\f=\frac{Tc}{b}$

So the peak frequency is directly proportional to the temperature in Kelvin.

In this problem, the temperature of the object changes from

$T_1 = 20.0^{\circ}+273=293 K$

to

$T_2 = 40.0^{\circ}+273 = 313 K$

so the peak frequency changes by a factor

$\frac{f_2}{f_1} \propto \frac{T_2}{T_1}=\frac{313 K}{293 K}=1.07$