(C) According to Stefan's law,the rate of energy emission (power) $Q$ from a black body is given by $Q = \sigma A T^4$.Here,$A$ is the surface area of

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$\left( \frac{Q}{4\pi \sigma R^2} \right)^{1/4}$

(C) According to Stefan's law,the rate of energy emission (power) $Q$ from a black body is given by $Q = \sigma A T^4$.Here,$A$ is the surface area of the star,which is $4\pi R^2$.Substituting the value of $A$ into the equation,we get $Q = \sigma (4\pi R^2) T^4$.Rearranging the formula to solve for temperature $T$,we have $T^4 = \frac{Q}{4\pi \sigma R^2}$.Taking the fourth root on both sides,we get $T = \left( \frac{Q}{4\pi \sigma R^2} \right)^{1/4}$.

Class 11 Physics 10-2.Heat Transfer Radiation by Stefan's Boltzmann Law

Medium

If the radius of a star is $R$ and it acts as a black body,what would be the temperature of the star,in which the rate of energy production is $Q$? ($\sigma$ stands for Stefan's constant)

AIPMT 2012 All AIPMT

A
$\frac{Q}{4\pi \sigma R^2}$
B
$\left( \frac{Q}{4\pi \sigma R^2} \right)^{1/2}$
C
$\left( \frac{Q}{4\pi \sigma R^2} \right)^{1/4}$
D
$\left( \frac{4\pi \sigma R^2}{Q} \right)^{1/4}$

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10-2.Heat Transfer

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Radiation by Stefan's Boltzmann Law

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If the radius of a star is $R$ and it acts as a black body,what would be the temperature of the star,in which the rate of energy production is $Q$? ($\sigma$ stands for Stefan's constant)

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The temperature of a piece of iron is $27^{\circ}C$ and it is radiating energy at the rate of $Q \text{ kW m}^{-2}$. If its temperature is raised to $151^{\circ}C$,the rate of radiation of energy will become approximately ....... $Q \text{ kW m}^{-2}$.

The ratio of radiant energies radiated per unit surface area by two bodies is $16 : 1$. The temperature of the hotter body is $1000 \ K$. Then,the temperature of the colder body will be ....... $K$.

$A$ black body surface with an area of $8 \ cm \times 4 \ cm$ emits energy at a rate of $E$ per second at a temperature of $127^{\circ}C$. If the length and width are halved and the temperature is increased to $327^{\circ}C$,find the new rate of energy emission.

Two spheres $P$ and $Q$,of the same color,having radii $8 \; cm$ and $2 \; cm$ are maintained at temperatures $127^{\circ}C$ and $527^{\circ}C$ respectively. The ratio of energy radiated by $P$ and $Q$ is:

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