Two spheres of radii 8 cm and 2 cm are cooling. Their temperatures are 127 ℃ and 527 ℃ respectively. The ratio of energy radiated by them in the same amount of time is

Question

Two spheres of radii 8 cm and 2 cm are cooling. Their temperatures are 127 ℃ and 527 ℃ respectively. The ratio of energy radiated by them in the same amount of time is (A) 0.06 (B) 0.5 (C) 1 (D) 2

Tardigrade Admin · Accepted Answer

Total energy radiated from a body Q=Aε σ T4t or (Q/t) propto AT4 (Q/t) propto r2T4 ( ∵ A=4π r2) (Q1/Q2)=((r1/r2))2 ((T1/T2))4 = ((8/2))2 ((273 + 127/273 + 527))4 = 1

Q. Two spheres of radii $8 c m$ and $2 c m$ are cooling. Their temperatures are $127 ℃$ and $527 ℃$ respectively. The ratio of energy radiated by them in the same amount of time is

$0.06$

$0.5$

$1$

$2$

Total energy radiated from a body
$Q = A ε σ T^{4} t$
or $\frac{Q}{t} \propto A T^{4}$
$\frac{Q}{t} \propto r^{2} T^{4}$ ( $∵ A = 4 π r^{2})$
$\frac{Q _{1}}{Q _{2}} = (\frac{r _{1}}{r _{2}})^{2} (\frac{T _{1}}{T _{2}})^{4}$
$= (\frac{8}{2})^{2} (\frac{273 + 127}{273 + 527})^{4} = 1$

Q. Two spheres of radii 8cm and 2cm are cooling. Their temperatures are 127℃ and 527℃ respectively. The ratio of energy radiated by them in the same amount of time is

0.06

0.5

1

2

Total energy radiated from a body Q=AεσT4t or tQ​∝AT4 tQ​∝r2T4 ( ∵A=4πr2) Q2​Q1​​=(r2​r1​​)2(T2​T1​​)4 =(28​)2(273+527273+127​)4=1

Q. Two spheres of radii $8 c m$ and $2 c m$ are cooling. Their temperatures are $127 ℃$ and $527 ℃$ respectively. The ratio of energy radiated by them in the same amount of time is

$0.06$

$0.5$

$1$

$2$

Total energy radiated from a body
$Q = A ε σ T^{4} t$
or $\frac{Q}{t} \propto A T^{4}$
$\frac{Q}{t} \propto r^{2} T^{4}$ ( $∵ A = 4 π r^{2})$
$\frac{Q _{1}}{Q _{2}} = (\frac{r _{1}}{r _{2}})^{2} (\frac{T _{1}}{T _{2}})^{4}$
$= (\frac{8}{2})^{2} (\frac{273 + 127}{273 + 527})^{4} = 1$