How is the temperature of the sun measured?

 After reading this question you might think about measuring sun’s temperature probably by sending some sort space probe with thermometer near sun which would do that, but we all know that's, not possible of course. 

So how do we do that. 

 

Let’s look at something interesting. 

 

Some of you might be aware about what radiation is, but there’s  nothing to worry about even if you don’t ,understand that radiation in simple words is defined as the transmission of energy from a body in the form of waves or particles. This can encompass anything from dangerous radiation created by a nuclear power plant to the harmless light created by a flashlight.There is a term called black body radiation, which means that a body which absorbs (and emits) all wavelengths of light and so appears black. 

 

Coming back to our question, how is temperature of the sun measured and the answer is by Wien’s Displacement Law or Stefan’s Boltzmann 

relation?

 

Wien’s displacement law  states that the wavelength for which the emission power of a black body is maximum is inversely proportional to the absolute temperature of the black body. Wien’s Displacement law equation is useful to find the temperatures of hot radiant bodies such as stars and used for finding the temperature of any radiant object which is far above that of its surroundings.According to Wien’s Displacement Law, 

λ(max) ∝ 1/T   

 

λ=b/T 

 

 

where, λ  is the wavelength,T is the temperature and 

 

b is Stefan Boltzmann constant whose value is 

 

2.898×10−3 mK. 

 

 

The wavelength of the peak of the black body 

 

radiation curve decreases in a linear fashion as the 

 

temperature is increased.

 

This linear variation is not evident in this kind of 

 

plot since the intensity increases with the fourth 

 

power of the temperature according to Stefan 

 

Boltzmann Law.

 

 

Since the temperature of the sun is high, its wavelength is minimum according to Wein’s Displacement Law so with the help of intensity of radiation we can calculate the temperature.

 

The sun is considered as a black body. Since the

 

light from the sun, we have seen from the surface 

 

has had nearly the spectrum of a black body. It 

 

implies that  emissivity(e) of the sun is 1(emissivity 

 

of black body is always 1).

 

Radiation spread out by the sun per square meter is 

 

estimated to be, I=1.36kW/m^2 

The radius of the sun is 7.0×10^5 km.

According to Stefan’s Boltzmann law, Q=eσ AT^4

Q is the power radiated by thermally emitting 

 

object, 4π d^2I

E is the emissivity power which is 1, σ is a constant, 

 

5.67 ×10^-8W/m^2K^4

A is the surface area(calculated from the radius) of 

 

the sun and

T is temperature of the sun.

Substituting the values by solving for T we get the 

 

value to be approximately 5760K(Kelvin)

T is approximately equal to 5800K