Answer:
it increases by a factor 1.07
Explanation:
The peak wavelength of an object is given by Wien's displacement law:
[tex]\lambda=\frac{b}{T}[/tex] (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:
[tex]f=\frac{c}{\lambda}[/tex]
where c is the speed of light, we can rewrite (1) as
[tex]\frac{c}{f}=\frac{b}{T}\\f=\frac{Tc}{b}[/tex]
So the peak frequency is directly proportional to the temperature in Kelvin.
In this problem, the temperature of the object changes from
[tex]T_1 = 20.0^{\circ}+273=293 K[/tex]
to
[tex]T_2 = 40.0^{\circ}+273 = 313 K[/tex]
so the peak frequency changes by a factor
[tex]\frac{f_2}{f_1} \propto \frac{T_2}{T_1}=\frac{313 K}{293 K}=1.07[/tex]
