A black sphere of radius R radiates power P a | 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 power $P$ radiated by a black body of surface area $A$ at temperature $T$ is given by $P = \sigma A T^4$

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(D) According to the Stefan-Boltzmann Law,the power $P$ radiated by a black body of surface area $A$ at temperature $T$ is given by $P = \sigma A T^4$.For a sphere of radius $R$,the surface area is $A = 4 \pi R^2$.Thus,the initial power is $P_1 = \sigma (4 \pi R^2) T^4$.When the radius is doubled $(R' = 2R)$ and the temperature is doubled $(T' = 2T)$,the new power $P_2$ is:$P_2 = \sigma (4 \pi (2R)^2) (2T)^4$$P_2 = \sigma (4 \pi \cdot 4R^2) (16T^4)$$P_2 = 16 \cdot 4 \cdot \sigma (4 \pi R^2) T^4$$P_2 = 64 P_1$.Therefore,the new power radiated is $64 P$.

$A$ black sphere of radius $R$ radiates power $P$ at a certain temperature $T$. If the temperature is doubled and the radius is also doubled,the new power radiated will be: (in $P$)

Similar Questions

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)

The temperature at which a black body of unit area loses its energy at the rate of $1 \text{ J/s}$ is:

When the temperature of a black body is increased, the value of $\lambda_m$ changes from $0.26 \mu m$ to $0.13 \mu m$. What is the ratio of its emissive power corresponding to these temperatures?

Two spheres of the same material have radii $1 \ m$ and $4 \ m$ and temperatures $4000 \ K$ and $2000 \ K$ respectively. The energy radiated per second by the first sphere is

$A$ body of area $1\, cm^2$ is heated to a temperature $1000\, K$. The amount of energy radiated by the body in $1\, second$ is .......... $Joule$ (Stefan's constant $\sigma = 5.67 \times 10^{-8}\, W\, m^{-2}K^{-4}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module