If temperature of a black body increases from $7°C$ to $287°\mathrm{C}$ , then the rate of energy radiation increases by

(a) ${\left(\frac{287}{7}\right)}^4$                  (b) 16
(c) 4                            (d) 2

The area of a hole of heat furnace is ${10}^{-4} {\mathrm{m}}^2$. It radiates $1.58\times {10}^5$ calories of heat per hour. If the emissivity of the furnace is 0.80, then its temperature is
(1) 1500 K           

(2) 2000 K

(3) 2500 K           

(4) 3000 K

Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperatures 127$°\mathrm{C}$and 527$°\mathrm{C}$ respectively. The ratio of energy radiated by P and Q is 
(a) 0.054             (b) 0.0034
(c) 1                   (d) 2

A body radiates energy 5W at a temperature of 127$°\mathrm{C}$. If the temperature is increased to 927$°\mathrm{C}$, then it radiates energy at the rate of
(a) 410 W                   (b) 81 W 
(c) 405 W                   (d) 200 W

The temperatures of two bodies A and B are respectively 727$°\mathrm{C}$ and 327$°\mathrm{C}$. The ratio of the rates of heat radiated by them is 

(1)727:327                       

(2) 5 : 3

(3) 25 : 9                           

(4) 625 : 81

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) $80 \mathrm{kcal}/{\mathrm{m}}^2\min$

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)  ${\left(300\right)}^4$