CSIR-NET 2015 June (112)

CSIR-NET 2015

112. Consider two planets A and B with the following characteristics. The relationship between T1 and T2 is..

Solution:

Distance from Radius of the Incident Equivalent

the Sun planet solar flux temperature

density

Planet A d₁ r₁ F₁ T₁

Planet B d₂= 4d₁ r₁= 2r₁ F₂ T₂

A) T₁= 2T₂

B) T₁= √2 T₂

C) T₁= 4T₂

D) T₂= 4T₁

Solution:

Luminosity is the total amount of energy emitted by star per unit time.

Two things determine the luminosity ( intrinsic brightness) of any star.

(1) Radius

(2) surface temperature

The Sun radius = 6,95,500 km , the surface temp= 5,830 K

Formula:

Luminosity = (radius)^{^2}*(Temperature)^⁴ ----------------(1)

L = R^{^2}* T^{^4}

T^{^4} α (1/R^²) ---------------(2)

Therefore, (T₁^{^4}/T₂^{^4}) = (R₂^{^2}/ R₁^{^2})

(T₁^{^4}/T₂^{^4}) =( 4R₁^{^2}/ R₁^{^2}) (from above data R₂ = 2R₁)

T₁ = 4T₂

GEOPHYSICS