The radiant energy from the sun incident normally at the surface of earth is $20 \mathrm{kcal}/{\mathrm{m}}^2\min$. What would have been the radiant energy incident normally on the earth, if the sun had a temperature twice of the present one ?

(a) $160 \mathrm{kcal}/{\mathrm{m}}^2\min$                    (b) $40 \mathrm{kcal}/{\mathrm{m}}^2\min$
(c) $320 \mathrm{kcal}/{\mathrm{m}}^2\min$                    (d) $80 \mathrm{kcal}/{\mathrm{m}}^2\min$

A spherical black body with a radius of 12 cm radiates 440 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be

(1) 225                     

(2) 450

(3) 900                     

(4) 1800

If the temperature of the sun (black body) is doubled, the rate of energy received on earth will be increased by a factor of 
(1) 2                         

(2) 4

(3) 8                         

(4) 16

The ratio of energy of emitted radiation of a black body at 27$°\mathrm{C}$ and 927$°\mathrm{C}$ is
(a) 1 : 4                  (b) 1 : 16
(c) 1 : 64                 (d) 1 : 256

Two spherical black bodies of radii ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ and with surface temperature ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ respectively radiate the same power. Then the ratio of ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ will be

(a) ${\left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)}^2$                (b) ${\left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)}^4$
(c) ${\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^2$                (d) ${\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^4$

A black body is at a temperature 300 K. It emits energy at a rate, which is proportional to

(a) 300             (b) ${\left(300\right)}^2$ 
(c) ${\left(300\right)}^3$         (d)  ${\left(300\right)}^4$

Two identical metal balls at temperature 200$°\mathrm{C}$ and 400$°\mathrm{C}$ kept in air at 27$°\mathrm{C}$. The ratio of net heat loss by these bodies is 
(1) 1/4     
           
(2) 1/2

(3) 1/16   
           
(4) $\frac{{473}^4-{300}^4}{{673}^4-{300}^4}$ 

The radiation emitted by a star A is 10,000 times that of the sun. If the surface temperatures of the sun and the star A are 6000 K and 2000 K respectively, the ratio of the radii of the star A and the sun is 
1. 300 : 1                     

2. 600 : 1

3. 900 : 1                     

4. 1200 : 1

Star A has radius r surface temperature T while star B has radius 4r and surface temperature T/2. The ratio of the power of two stars, ${\mathrm{P}}_{\mathrm{A}}$:${\mathrm{P}}_{\mathrm{B}}$is 
(1) 16 : 1                           

(2) 1 : 16

(3) 1 : 1                             

(4) 1 : 4

Suppose the sun expands so that its radius becomes 100 times its present radius and its surface temperature becomes half of its present value. The total energy emitted by it then will increase by a factor of
(1) ${10}^4$                

(2) 625

(3) 256                 

(4) 16