The wavelength of maximum intensity of radiat | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given: $\lambda_m = 289.8 \ nm = 289.8 	imes 10^{-9} \ m$.Wien's constant $b = 2898 \ \mu m \ K = 2898 	imes 10^{-6} \ m \ K$.Stefan's constant

Vedclass · Accepted Answer

$5.67 	imes 10^8 \ W/m^2$

Vedclass · Answer

(A) Given: $\lambda_m = 289.8 \ nm = 289.8 	imes 10^{-9} \ m$.Wien's constant $b = 2898 \ \mu m \ K = 2898 	imes 10^{-6} \ m \ K$.Stefan's constant $\sigma = 5.67 	imes 10^{-8} \ W m^{-2} K^{-4}$.From Wien's displacement law, $\lambda_m T = b$.Therefore, the temperature of the star is $T = \frac{b}{\lambda_m} = \frac{2898 	imes 10^{-6}}{289.8 	imes 10^{-9}} = \frac{2898 	imes 10^{-6}}{289.8 	imes 10^{-9}} = 10^4 \ K$.The radiation intensity (emissive power) $E$ is given by Stefan-Boltzmann law: $E = \sigma T^4$.$E = (5.67 	imes 10^{-8}) 	imes (10^4)^4$.$E = 5.67 	imes 10^{-8} 	imes 10^{16}$.$E = 5.67 	imes 10^8 \ W/m^2$.

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \ nm$. The radiation intensity of the star is (Stefan's constant $= 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$, Wien's constant $b = 2898 \ \mu m \ K$).

Similar Questions

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

$A$ black body radiates energy at the rate of $1 \times 10^5 \ J/s \cdot m^2$ at a temperature of $227^\circ C$. The temperature to which it must be heated so that it radiates energy at a rate of $1 \times 10^9 \ J/s \cdot m^2$ is:

$A$ black body of surface area $10 \ cm^2$ is heated to $127^{\circ}C$ and is suspended in a room at temperature $27^{\circ}C$. The initial rate of loss of heat from the body at the room temperature will be ...... $W$.

$A$ black body is heated from $27^oC$ to $127^oC$. The ratio of their energies of radiations emitted will be

Two spheres of same material and radii $5 \ m$ and $2 \ m$ are at temperatures $200 \ K$ and $250 \ K$ respectively. The ratio of energies radiated by them per second is

Vedclass Test Series

Exam Paper Generator

Online Exam Module