A particular star (assuming it as a black body) has a surface temperature of about $5\times {10}^4 \mathrm{K}$. The wavelength in nanometers at which its radiation becomes maximum is -
(b = 0.0029 mK) 
(1) 48               

(2) 58

(3) 60                 

(4) 70

The intensity of radiation emitted by the sun has its maximum value at a wavelength of 510 nm and that emitted by the north star has the maximum value at 350 nm. If these stars behave like black bodies, then the ratio of the surface temperature of the sun and north star is

(1) 1.46                 

(2) 0.69

(3) 1.21                 

(4) 0.83

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 $1.0\times {10}^6 \mathrm{J}/\sec -{\mathrm{m}}^2$. Temperature of the black body at which the rate of energy emission is $16.0\times {10}^6 \mathrm{J}/\sec -{\mathrm{m}}^2$ 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 ${10}^{-4} {\mathrm{m}}^2$. 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