A spherical black body of radius 12 , cm radi | vedclass

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

Question

(D) The power radiated by a black body is given by the Stefan-Boltzmann law: $P = A \sigma T^4 = 4 \pi r^2 \sigma T^4$.From this,we can see that $P \p

Vedclass · Accepted Answer

$1800$

Vedclass · Answer

(D) The power radiated by a black body is given by the Stefan-Boltzmann law: $P = A \sigma T^4 = 4 \pi r^2 \sigma T^4$.From this,we can see that $P \propto r^2 T^4$.Let the initial radius be $r_1 = 12 \, cm$ and initial temperature be $T_1 = 500 \, K$. The initial power is $P_1 = 450 \, W$.For the new state,the radius is halved,so $r_2 = r_1 / 2$,and the temperature is doubled,so $T_2 = 2 T_1$.Taking the ratio of the powers:$\frac{P_2}{P_1} = \left( \frac{r_2}{r_1} ight)^2 \left( \frac{T_2}{T_1} ight)^4$$\frac{P_2}{P_1} = \left( \frac{1}{2} ight)^2 \left( \frac{2}{1} ight)^4 = \frac{1}{4} 	imes 16 = 4$.Therefore,$P_2 = 4 P_1 = 4 	imes 450 = 1800 \, W$.

$A$ spherical black body of radius $12 \, cm$ radiates $450 \, W$ of power at $500 \, K$. If the radius is halved and the temperature is doubled,the power radiated will be ..... $W$.

Similar Questions

Find the rate of radiation emitted per unit area per unit time by a black body at a temperature of $10^{3} \ K$ (in $J \ m^{-2} \ s^{-1}$).

The temperature of a black body reduces to half of its initial value. By what fraction will the amount of radiation emitted reduce?

$A$ black sphere has radius $R$ whose rate of radiation is $E$ at temperature $T$. If the radius is made half and the temperature is made $4T$,the rate of radiation will be: (in $E$)

$A$ 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 ...... $W$.

The spectral energy distribution of a star is maximum at a temperature twice that of the Sun. The total energy radiated by the star is

Vedclass Test Series

Exam Paper Generator

Online Exam Module