Parallel rays of light of intensity $I =912 \ Wm ^{-2}$ are incident on a spherical balck body kept in surroundings of temperature $300 \ K$. Take Stefan-Boltzmann constant $\sigma=5.7 \times 10^{-8} Wm ^{-2} K ^{-4}$ and assume that the energy exchange with the surroundings is only through radiation. Th final steady state temperature of the black body is close to:
IIT 2014, Diffcult
Download our app for free and get started
In steady state
$I \pi R ^2= $$ \sigma\left( T ^4- T _0^4\right) 4 \pi R ^2$
$\Rightarrow $$ I =\sigma\left( T ^4- T _0^4\right) 4$
$\Rightarrow $$ T ^4- T _0^4=40 \times 10^8$
$\Rightarrow $$ T ^4-81 \times 10^8=40 \times 10^8$
$\Rightarrow $$ T ^4=121 \times 10^8$
$\Rightarrow $$ T \approx 330 K$
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
- 1A copper rod $2\,m$ long has a circular cross-section of radius $1\, cm$. One end is kept at $100^o\,C$ and the other at $0^o\,C$ and the surface is covered by nonconducting material to check the heat losses through the surface. The thermal resistance of the bar in degree kelvin per watt is (Take thermal conductivity $K = 401\, W/m-K$ of copper):-View Solution
- 2Two 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 isView Solution
- 3The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$ , respectively are $T_2$ and $T_1$ ($T_2$ > $T_1$). The rate of heat transfer through the slab, in a steady state is $\left( {\frac{{A({T_2} - {T_1})K}}{x}} \right)f$, with $f $ which equal toView Solution
- 4A black body at $200 K$ is found to exit maximum energy at a wavelength of $14\mu m$. When its temperature is raised to $1000K$ , the wavelength at which maximum energy is emitted isView Solution
- 5A composite metal bar of uniform section is made up of length $25 cm$ of copper, $10 cm$ of nickel and $15 cm$ of aluminium. Each part being in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at ${100^o}C$ and the aluminium end at ${0^o}C$. The whole rod is covered with belt so that there is no heat loss occurs at the sides. If ${K_{{\rm{Cu}}}} = 2{K_{Al}}$ and ${K_{Al}} = 3{K_{{\rm{Ni}}}}$, then what will be the temperatures of $Cu - Ni$ and $Ni - Al$ junctions respectivelyView Solution
- 6View SolutionRelation between the colour and the temperature of a star is given by
- 7Two thin metallic spherical shells of radii ${r}_{1}$ and ${r}_{2}$ $\left({r}_{1}<{r}_{2}\right)$ are placed with their centres coinciding. A material of thermal conductivity ${K}$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}\left(\theta_{1}<\theta_{2}\right)$. The rate at which heat flows radially through the material is :-View Solution
- 8Three rods of the same dimension have thermal conductivities $3K$ , $2K$ and $K$ . They are arranged as shown in fig. Given below, with their ends at $100^oC, 50^oC $and $20^oC$. The temperature of their junction is ......... $^oC$View Solution
- 9The ratio of energy of emitted radiation of a black body at ${27^o}C$ and ${927^o}C$ isView Solution
- 10A black metal foil is warmed by radiation from a small sphere at temperature $T$ and at a distance $d$. It is found that the power received by the foil is $`P$ '. If both the temperature and the distance are doubled, the power received by the foil will beView Solution