The power radiated by a black body is $P$ and it radiates maximum energy at wavelength,$\lambda_0.$ If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4}\lambda_0$, the power radiated by it becomes $nP$. The value of $n$ is
NEET 2018,AIIMS 2001, Medium
Download our app for free and get started
From $Wien's$ law, ${\lambda _{\max }}T = constant$
So, ${\lambda _{{{\max }_1}}}{T_1} = {\lambda _{{{\max }_2}}}{T_2}$
$ \Rightarrow {\lambda _0}T = \frac{{3{\lambda _0}}}{4}T' \Rightarrow \frac{{T'}}{T} = \frac{4}{3}$ $...(i)$
According to $Stefan-Boltzmann\,law$, energy emitted unit time by a blck body is $Ae\sigma T',i.e.,$ power radiated,
$\therefore \,\,P \propto {T^4}$
$So,\frac{{{P_2}}}{{{P_1}}} = {\left( {\frac{{T'}}{T}} \right)^4} \Rightarrow n = {\left( {\frac{4}{3}} \right)^4} = \frac{{256}}{{81}}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two spherical stars $A$ and $B$ emit blackbody radiation. The radius of $A$ is $400$ times that of $B$ and $A$ emits $10^4$ times the power emitted from $B$. The ratio $\left(\lambda_A / \lambda_B\right)$ of their wavelengths $\lambda_A$ and $\lambda_B$ at which the peaks occur in their respective radiation curves isView Solution
- 2The sun emits a light with maximum wavelength $510\, mm$ while another star $X$ emits a light with maximum wavelength of $350\, nm$. What is the ratio of surface temperature of sun and the star $X$View Solution
- 3View SolutionThe Wien’s displacement law express relation between
- 4A black body radiates at the rate of $W$ watts at a temperature $T$ . If the temperature of the body is reduced to $T/3$ , it will radiate at the rate of (in Watts)View Solution
- 5Radiation from a black body at the thermodynamic temperature $T_1$ is measured by a small detector at distance $d_1$ from it. When the temperature is increased to $T_2$ and the distance to $d_2$ , the power received by the detector is unchanged . What is the ratio $d_2/d_1$ ?View Solution
- 6Heat is flowing through a conductor of length l from $x = 0$ to $x = l$ . If its thermal resistance per unit length is uniform, which of the following graphs is correctView Solution
- 7View SolutionCooling law is based upon
- 8A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at $0 K$. At time $t =0$, the temperature of the object is $200 K$. The temperature of the object becomes $100 K$ at $t = t _1$ and $50 K$ at $t = t _2$. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio $\left( t _2 / t _1\right)$ is. . . . .View Solution
- 9View SolutionIf a liquid is heated in weightlessness, the heat is transmitted through
- 10An insulated container is filled with ice at $0\,^oC$ , and another container is filled with water that is continuously boiling at $100\,^oC$ . In series of experiments, the containers are connected by various thick metal rods that pass through the walls of container as shown in the figureView Solution
In the experiment $I$ : a copper rod is used and all ice melts in $20$ minutes.
In the experiment $II$ : a steel rod of identical dimensions is used and all ice melts in $80$ minutes.
In the experiment $III$ : both the rods are used in series and all ice melts in $t_{10}$ minutes.
In the experiment $IV$ : both rods are used in parallel and all ice melts in $t_{20}$ minutes.
