Question

As the heating element on a stove top gets hotter, it begins to glow at visible wavelengths.

a) What temperature must the heating element achieve to glow most brightly at red wavelengths of 700 nm?

b) What temperature must the heating element achieve to glow most brightly at blue wavelengths of 450 nm?

c) Typically, home appliances are color coded such that red represents hot settings and blue represents cold settings. Why might this color coding seem backwards to a zealous physicist? Why does this color coding seem perfectly logical to everyone else?

Answer 1

Wien's displacement law is used to find the temperatures of hot radiant objects.

According to this law , wavelength corresponding to maximum radiation emitted is inversely proportional to the temperature of the object.

If is the wavelength and T is the temperature of the object , we can write

   1 / T

   T = b

where b = 2.898 × 10^-3 m K is the wien's constant.

a) Given that wavelength = 700 n m = 700 × 10^-9 m

Temperature of the object is T_a = b /

= ( 2.898 × 10^-3 ) / ( 700 × 10^-9 )

= 4.14 × 10³ K

= 4140 K

So for the object to glow red , it must have a temperature of 4140 K

b) Wavelength corresponding to blue light is = 450 nm

= 450 × 10^-9 m

Temperature of the object T_b = b /

= ( 2.898 × 10^-3/ 450 × 10^-9 )

= 6.440 × 10³ K

= 6440 K

So for the heating element to glow blue , it must have a temperature 6440 K

C) Color coding is not acceptable for a physicist . We can clearly observe from the above calculation that temperature required for the element to glow blue is more than that is required for red color.

So for a physicist blue must be used to represent hot settings.

For others , red color represents danger and so generally red color is used to represent hot settings indicating that if the hot object is left the same way it might lead to a problem by burning or causing any other damage. So this color coding seems logical for common people.