Two spherical black bodies have radii âr1â and 'r2' . Their surface temperatures are 'T1' and 'T2'. If they radiate same power then (r2/r1) is

Question

Two spherical black bodies have radii âr1â and 'r2' . Their surface temperatures are 'T1' and 'T2'. If they radiate same power then (r2/r1) is (A) (T1/T2) (B) (T2/T1) (C) ((T1/T2))2 (D) ((T2/T1))2

Tardigrade Admin · Accepted Answer

P 1= A σ T 14=π r 12 σ T 14 P 2= A σ T 24=π r 22 σ T 24 P 1= P 2 so ( r 2/ r 1)=( T 12/ T 22)

Q. Two spherical black bodies have radii $‘ r_{1} ’$ and $^{'} r_{2}^{'}$ . Their surface temperatures are $^{'} T_{1}^{'}$ and $^{'} T_{2}^{'}$ . If they radiate same power then $\frac{r _{2}}{r _{1}}$ is

$\frac{T _{1}}{T _{2}}$

$\frac{T _{2}}{T _{1}}$

$(\frac{T _{1}}{T _{2}})^{2}$

$(\frac{T _{2}}{T _{1}})^{2}$

$P_{1} = A σ T_{1}^{4} = π r_{1}^{2} σ T_{1}^{4}$
$P_{2} = A σ T_{2}^{4} = π r_{2}^{2} σ T_{2}^{4}$
$P_{1} = P_{2}$
so $\frac{r _{2}}{r _{1}} = \frac{T _{1}^{2}}{T _{2}^{2}}$

Q. Two spherical black bodies have radii ‘r1​’ and ′r2′​ . Their surface temperatures are ′T1′​ and ′T2′​. If they radiate same power then r1​r2​​ is

T2​T1​​

T1​T2​​

(T2​T1​​)2

(T1​T2​​)2