Question

Suppose the surface temperature of the Sun was 12,000 K, rather than 6000 K.

a) How much more thermal radiation would the Sun emit?

b) What would happen to the Sun's wavelength of peak emission? Do you think it would still be possible to have life on Earth? Explain.

Answer 1

a) In order to calculate the emitted power per square meter we need to use Stefan-Boltzmann’s Law

E = σ*T⁴

Where E = Emitted Power per square meter of surface

T = Temperature in kelvin (K) and σ = Stefan-Boltzmann Constant = 5.7*10^-8 watt m^-2K^-4

At 6000 K

Emitted power (E) = σ*(6000 K)⁴...........(i)

At 12000 K

Emitted power (E) = σ*(12000 K)⁴..........(ii)

Now calculate the ratio of thermal radition at two different temperature in order to get how much thermal radiation would sun emit

Divide (ii) by (i)

E_1200K / E_6000K = σ*(12000 K)⁴/σ*(6000 K)⁴ = (12000/6000)⁴ = 2⁴ =16

Therefore, E_1200K / E_6000K = 16

Therefore, emitted power of sun at 12000K is 16 times more than the emitted power at 6000K

b) To calculate the wavelength of maximum intensity we need to use Wien’s Law, that is​

λ_max = b/T

Where λ_max = wavelength of maximum intensity

b = wien's constant = 2,900,000 nm.K

T = Temperature in Kelvin(K)

At 6000K λ_max = 2,900,000/6000 = 483.33 nm

At 12000K λ_max = 2,900,000/12000 = 241.67 nm

Ratio = ( λ_{max at 12000K}/ λ_{max at 6000K}) = 0.5 or 1/2

Therefore, wavelength of maximum intensity at 12000K is half the wavelength of the maximum intensity at 6000K

Therefore, at 12000 K temperature the sun will emits ultraviolet light which is not suitable for living.

As intensity of light emitted by a given object depends on its frequency or wavelength and the wavelength at given temperature 12,000K is reduced by half which means its frequency has increased by half and as we known that EM spectrum contain UV rays at shorter wavelengths. Thus, not suitable for living.