The total radiant energy per unit area, normal to the direction of incidence, received at a distance R from the center of a star of radius r, whose outer surface radiates as a black body at a temperature T K is given by (where σ is Stefan's constant)

Question

The total radiant energy per unit area, normal to the direction of incidence, received at a distance R from the center of a star of radius r, whose outer surface radiates as a black body at a temperature T K is given by (where σ is Stefan's constant) (A) (σ r2T4/R2) (B) (σ r2T4/4π r2) (C) (σ r4T4/r4) (D) (4πσ r2T4/R2)

Tardigrade Admin · Accepted Answer

By Stefan's law, E =σ e AT 4 For black body, e = 1 Energy, E =σ(4 π r 2) T 4 Intensity, I =(σ(4 π r 2 T 4)/4 π R 2)=(σ r 2 T 4/ R 2)

Q. The total radiant energy per unit area, normal to the direction of incidence, received at a distance $R$ from the center of a star of radius $r$ , whose outer surface radiates as a black body at a temperature $T K$ is given by (where $σ$ is Stefan's constant)

$\frac{σ r ^{2} T ^{4}}{R ^{2}}$

$\frac{σ r ^{2} T ^{4}}{4 π r ^{2}}$

$\frac{σ r ^{4} T ^{4}}{r ^{4}}$

$\frac{4 πσ r ^{2} T ^{4}}{R ^{2}}$

By Stefan's law,
$< b r / > E = σ e A T^{4} < b r / >$
For black body, e = 1
Energy, $E = σ (4 π r^{2}) T^{4}$
Intensity, $I = \frac{σ ( 4 π r ^{2} T ^{4} )}{4 π R ^{2}} = \frac{σ r ^{2} T ^{4}}{R ^{2}}$

Q. The total radiant energy per unit area, normal to the direction of incidence, received at a distance R from the center of a star of radius r, whose outer surface radiates as a black body at a temperature TK is given by (where σ is Stefan's constant)

R2σr2T4​

4πr2σr2T4​

r4σr4T4​

R24πσr2T4​