Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively., The ratio of energy radiated per second by the first sphere to the second is

Question

Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively., The ratio of energy radiated per second by the first sphere to the second is (A)  1: 1  (B)  16: 1  (C)  4: 1  (D)  1: 9

Tardigrade Admin · Accepted Answer

Energy radiated per second by a body which has surface area

A

at temperature

T

is given by Stefan's law,

E = σ A T^{4}

Therefore

\frac{E _{1}}{E _{2}} = (\frac{r _{1}}{r _{2}})^{2} (\frac{T _{1}}{T _{2}})^{4}

= (\frac{1}{4})^{2} (\frac{4000}{2000})^{4}

\frac{E _{1}}{E _{2}} = \frac{16}{16} = \frac{1}{1}

Q. Two spheres of the same material have radii $1 m$ and $4 m$ and temperatures $4000 K$ and $2000 K$ respectively., The ratio of energy radiated per second by the first sphere to the second is

$1 : 1$

$16 : 1$

$4 : 1$

$1 : 9$

Q. Two spheres of the same material have radii 1m and 4m and temperatures 4000K and 2000K respectively., The ratio of energy radiated per second by the first sphere to the second is

1:1

16:1

4:1

1:9

Energy radiated per second by a body which has surface area A at temperature T is given by Stefan's law, E=σAT4 Therefore E2​E1​​=(r2​r1​​)2(T2​T1​​)4 =(41​)2(20004000​)4 E2​E1​​=1616​=11​

Q. Two spheres of the same material have radii $1 m$ and $4 m$ and temperatures $4000 K$ and $2000 K$ respectively., The ratio of energy radiated per second by the first sphere to the second is

$1 : 1$

$16 : 1$

$4 : 1$

$1 : 9$