A black sphere has radius R whose rate of rad | vedclass

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

Question

(D) According to the Stefan-Boltzmann law,the rate of radiation $E$ from a black body is given by $E = A \sigma T^4$,where $A$ is the surface area,$\s

Vedclass · Accepted Answer

$9 E$

Vedclass · Answer

(D) According to the Stefan-Boltzmann law,the rate of radiation $E$ from a black body is given by $E = A \sigma T^4$,where $A$ is the surface area,$\sigma$ is the Stefan-Boltzmann constant,and $T$ is the absolute temperature.For a sphere,the surface area $A = 4 \pi R^2$.Thus,$E = (4 \pi R^2) \sigma T^4$,which implies $E \propto R^2 T^4$.Let the initial state be $E_1 = E$,$R_1 = R$,and $T_1 = T$.Let the final state be $E_2$,$R_2 = R/3$,and $T_2 = 3T$.Taking the ratio: $\frac{E_2}{E_1} = \left( \frac{R_2}{R_1} ight)^2 \left( \frac{T_2}{T_1} ight)^4$.Substituting the values: $\frac{E_2}{E} = \left( \frac{R/3}{R} ight)^2 \left( \frac{3T}{T} ight)^4$.$\frac{E_2}{E} = \left( \frac{1}{3} ight)^2 	imes (3)^4 = \frac{1}{9} 	imes 81 = 9$.Therefore,$E_2 = 9E$.

$A$ black sphere has radius $R$ whose rate of radiation is $E$ at temperature $T$. If the radius is made $R/3$ and the temperature $3T$,the rate of radiation will be:

Similar Questions

$A$ body emits $5 \ W$ of energy at a temperature of $127^{\circ}C$. If the temperature is increased to $927^{\circ}C$,then the emitted energy becomes .......... $W$.

$A$ metal ball of surface area $200 \; cm^2$ and temperature $527^{\circ}C$ is surrounded by a vessel at $27^{\circ}C$. If the emissivity of the metal is $0.4$,then the rate of loss of heat from the ball is approximately .......... $J/s$. $(\sigma = 5.67 \times 10^{-8} \; J/(m^2 \cdot s \cdot K^4))$

Compare the rate of loss of heat from a metal sphere at $627^{\circ} C$ with the rate of loss of heat from the same sphere at $327^{\circ} C$,if the temperature of the surrounding is $27^{\circ} C$. (nearly)

Two spheres of radii $8 \ cm$ and $2 \ cm$ are cooling. Their temperatures are $127^{\circ} C$ and $527^{\circ} C$ respectively. Find the ratio of energy radiated by them in the same time.

$A$ hot metallic sphere of radius $r$ radiates heat. Its rate of cooling is

Vedclass Test Series

Exam Paper Generator

Online Exam Module