A spherical black body with a radius of \(12\) cm radiates \(450\)-watt power at \(500\) K. If the radius were halved and the temperature doubled, the power radiated in watts would be:
1. \(225\)
2. \(450\)
3. \(1000\)
4. \(1800\)

The total radiant energy per unit area per unit time, normal to the direction of incidence, received at a distance R from the centre of a star of radius r,whose outer surface radiates as a black body at a temperature TK is given by 

(a) $\sigma r^2{T}^4/R^2$                                       (b) $\sigma r^2{T}^4/4{\mathrm{\pi r}}^2$

(c) $\sigma r^4{T}^4/r^4$                                        (d) $4\mathrm{\pi }<mspace\; width="1em"></mspace>\sigma r^2{T}^4/R^2$

(where $\sigma$ is Stefan's constant)

A black body at $227°C$ radiates heat at the rate of 7 cal $c{m}^{-2}{s}^{-1}.$ At a temperature of $727°C,$ the rate of heat radiated in the same units will be 

1. 60                                     

2. 50

3. 112                                   

4. 80

Which of the following law states that “good absorbers of heat are good emitters”  ?
(1) Stefan’s law               

(2) Kirchoff’s law

(3) Planck’s law               

(4) Wein’s law

The amount of radiation emitted by a perfectly black body is proportional to 

(1) Temperature on ideal gas scale

(2) Fourth root of temperature on ideal gas scale

(3) Fourth power of temperature on ideal gas scale

(4) Source of temperature on ideal gas scale

The temperature of an object is \(400^{\circ}\mathrm{C}\)$\mathrm{}$. The temperature of the surroundings may be assumed to be negligible. What temperature would cause the energy to radiate twice as quickly? (Given, \(2^{\frac{1}{4}} \approx 1.18\))
1. \(200^{\circ}\mathrm{C}\)
2. \(200\) K
3. \(800^{\circ}\mathrm{C}\)$\mathrm{}$         
4. \(800\) K

A black body at a temperature of 227$°\mathrm{C}$ radiates heat energy at the rate of 5 $\mathrm{cal}/{\mathrm{cm}}^2-\sec$. At a temperature of $727°\mathrm{C}$, the rate of heat radiated per unit area in $\mathrm{cal}/{\mathrm{cm}}^2$ will be 
(1) 80                     

(2) 160

(3) 250                   

(4) 500

Energy is being emitted from the surface of a black body at 127$°\mathrm{C}$ temperature at the rate of $1.0\times {10}^6<mspace\; width="1em"></mspace>\mathrm{J}/\sec -{\mathrm{m}}^2$. Temperature of the black body at which the rate of energy emission is $16.0\times {10}^6<mspace\; width="1em"></mspace>\mathrm{J}/\sec -{\mathrm{m}}^2$ will be -

(a) 254$°\mathrm{C}$          (b) 508$°\mathrm{C}$
(c) 527$°\mathrm{C}$          (d) 727$°\mathrm{C}$

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 ${10}^{-4}<mspace\; width="1em"></mspace>{\mathrm{m}}^2$. 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