Two spheres of the same material have radii r | vedclass

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

Question

(A) According to the Stefan-Boltzmann law,the total power $P$ radiated by a sphere of radius $r$ and temperature $T$ is given by $P = A \sigma T^4$,wh

Vedclass · Accepted Answer

$(\frac{T_2}{T_1})^2$

Vedclass · Answer

(A) According to the Stefan-Boltzmann law,the total power $P$ radiated by a sphere of radius $r$ and temperature $T$ is given by $P = A \sigma T^4$,where $A = 4 \pi r^2$ is the surface area and $\sigma$ is the Stefan-Boltzmann constant.Since the material is the same,the emissivity is the same. Given that the total power radiated $P$ is the same for both spheres,we have $P_1 = P_2$.Substituting the formula: $4 \pi r_1^2 \sigma T_1^4 = 4 \pi r_2^2 \sigma T_2^4$.Simplifying the equation: $r_1^2 T_1^4 = r_2^2 T_2^4$.Rearranging to find the ratio of radii: $(\frac{r_1}{r_2})^2 = (\frac{T_2}{T_1})^4$.Taking the square root on both sides: $\frac{r_1}{r_2} = (\frac{T_2}{T_1})^2$.

Two spheres of the same material have radii $r_1$ and $r_2$ and surface temperatures $T_1$ and $T_2$ respectively. If their emissive power (total power radiated) is the same,find the ratio of their radii $r_1/r_2$.

Similar Questions

$A$ wire of length $L$ and diameter $d$ is used in a bulb. The temperature of the wire is $T$ and the power radiated by the wire is $P$. Its emissivity is $e$ ($\sigma$ = Stefan's constant). (Assume that the emissivity of the wire material is the same at all wavelengths).

$A$ rectangular block of surface area $A$ emits energy $E$ per second at $27^{\circ} C$. If length and breadth are reduced to half of their initial values and the temperature is raised to $327^{\circ} C$,then the energy emitted per second becomes:

The energy spectrum of a black body has maximum energy at a wavelength of $\lambda_0$. Now, the temperature of the black body is increased such that the maximum energy is obtained at a wavelength of $3\lambda_0/4$. By what factor will the power radiated by the black body increase?

Solar constant $(S)$ depends upon the temperature of the Sun $(T)$ as ........

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module