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

If the temperature of the body is increased from \(-73^{\circ}\mathrm{C}\)$\mathrm{}$ to \(327^{\circ}\mathrm{C}\)$\mathrm{}$, then the ratio of energy emitted per second in both cases is:
1. 1 : 3                         
2. 1 : 81
3. 1 : 27                       
4. 1 : 9

If the sun’s surface radiates heat at \(6.3\times 10^{7}~\text{Wm}^{-2}\) ${\mathrm{}}^{}$then the temperature of the sun, assuming it to be a black body, will be:
\(\left(\sigma = 5.7\times 10^{-8}~\text{Wm}^{-2}\text{K}^{-4}\right)\)
1. \(5.8\times 10^{3}~\text{K}\)
2. \(8.5\times 10^{3}~\text{K}\)
3. \(3.5\times 10^{8}~\text{K}\)
4. \(5.3\times 10^{8}~\text{K}\)

The value of Stefan’s constant is 
(a) $5.67\times {10}^{-8} \mathrm{W}/{\mathrm{m}}^2-{\mathrm{K}}^4$                       (b) $5.67\times {10}^{-5} \mathrm{W}/{\mathrm{m}}^2-{\mathrm{K}}^4$
(c) $5.67\times {10}^{-11} \mathrm{W}/{\mathrm{m}}^2-{\mathrm{K}}^4$                      (d) None of these

Rate of cooling at 600K, if surrounding temperature is 300K is R. The rate of cooling at 900K is
(1) $\frac{16}{3}\mathrm{R}$                    

(2) 2R

(3) 3R                         

(4) $\frac{2}{3}\mathrm{R}$