A black metal foil is warmed by radiation fro | vedclass

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

Question

(B) The power $P$ received by a small area at a distance $d$ from a spherical source at temperature $T$ is proportional to the Stefan-Boltzmann law an

Vedclass · Accepted Answer

$4 P$

Vedclass · Answer

(B) The power $P$ received by a small area at a distance $d$ from a spherical source at temperature $T$ is proportional to the Stefan-Boltzmann law and the inverse square law of radiation.According to the Stefan-Boltzmann law,the total power radiated by the sphere is $P_{source} \propto T^4$.The intensity of radiation at a distance $d$ follows the inverse square law,$I \propto \frac{1}{d^2}$.Thus,the power received by the foil is $P \propto \frac{T^4}{d^2}$.Let the initial state be $P_1 = k \frac{T^4}{d^2} = P$.In the final state,the temperature becomes $T' = 2T$ and the distance becomes $d' = 2d$.The new power $P'$ is given by:$P' = k \frac{(2T)^4}{(2d)^2} = k \frac{16 T^4}{4 d^2} = 4 \left( k \frac{T^4}{d^2} \right) = 4P$.

$A$ 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 distance are doubled,the power received by the foil will be:

Similar Questions

Find the radiant energy emitted per second in $Js^{-1}$ by a lamp filament at $2000 K$. The surface area is $5.0 \times 10^{-5} m^{2}$,the relative emissivity is $0.85$,and $\sigma = 5.7 \times 10^{-8} W m^{-2} K^{-4}$.

Star $A$ has radius $r$ and surface temperature $T$,while star $B$ has radius $4r$ and surface temperature $T/2$. The ratio of the power radiated by the two stars,$P_A : P_B$,is:

The distance between the Sun and the Earth is $2 \times 10^{8} \ km$, the temperature of the Sun is $6000 \ K$, and the radius of the Sun is $7 \times 10^{5} \ km$. If the emissivity of the Earth is $0.6$, find the temperature of the Earth in thermal equilibrium (in $K$).

The heat radiated per unit area in $1\,hour$ by a furnace whose temperature is $3000\,K$ is $(\sigma = 5.7 \times 10^{-8}\,W\,m^{-2}\,K^{-4})$.

$A$ cube of side $1 \ m$ has a temperature of $127^{\circ}C$ and an emissivity of $\frac{1}{5.67}$. If the surrounding temperature is $27^{\circ}C$,the rate of loss of heat by radiation is ...... $kW$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module