Two metal spheres have radii r and 2r and the | vedclass

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

Question

(A) According to Wien's displacement law, $\lambda_m T = 	ext{constant} (b)$.For the first sphere: $\lambda T_1 = b \implies T_1 = \frac{b}{\lambda}$

Vedclass · Accepted Answer

$4: 1$

Vedclass · Answer

(A) According to Wien's displacement law, $\lambda_m T = 	ext{constant} (b)$.For the first sphere: $\lambda T_1 = b \implies T_1 = \frac{b}{\lambda}$.For the second sphere: $(2\lambda) T_2 = b \implies T_2 = \frac{b}{2\lambda} = \frac{T_1}{2}$.The radiant energy emitted per second is the power $P = \sigma A T^4 = \sigma (4\pi R^2) T^4$.Thus, $P \propto R^2 T^4$.Calculating the ratio $\frac{P_1}{P_2} = \left( \frac{r_1}{r_2} ight)^2 \left( \frac{T_1}{T_2} ight)^4$.Substituting the values: $\frac{P_1}{P_2} = \left( \frac{r}{2r} ight)^2 \left( \frac{T_1}{T_1/2} ight)^4 = \left( \frac{1}{2} ight)^2 (2)^4 = \frac{1}{4} 	imes 16 = 4$.Therefore, the ratio is $4: 1$.

Two metal spheres have radii $r$ and $2r$ and they emit thermal radiation with maximum intensities at wavelengths $\lambda$ and $2\lambda$ respectively. The respective ratio of the radiant energy emitted by them per second will be .........

Similar Questions

The temperature of a furnace is $200\,^{\circ}C$. In its spectrum,the maximum intensity is obtained at about $400\,\mathring{A}$. If the maximum intensity is at $200\,\mathring{A}$,calculate the temperature of the furnace in $^{\circ}C$. ......... $^{\circ}C$

$A$ black body emits radiation with maximum intensity at a wavelength of $5000 \mathring{A}$ at a temperature of $1227^\circ C$. If its temperature is increased by $1000^\circ C$, the new wavelength of maximum intensity will be ...... $\mathring{A}$.

Two stars emit maximum radiation at wavelengths $3600 \mathring A$ and $4800 \mathring A$ respectively. The ratio of their temperatures is:

$A$ black body at $1227^{\circ}C$ emits radiations with maximum intensity at a wavelength of $5000\;\mathring{A}$. If the temperature of the body is increased by $1000^{\circ}C$,the maximum intensity will be observed at ...... $\mathring{A}$.

Assume that for solar radiation,the surface temperature of the Sun is $6000 \,K$. If Wien's constant '$b$' is $2.897 \times 10^{-3} \,m-K$,the value of the maximum wavelength will be: (in $Å$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module