Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperature 127° C and 527° C respectively. The ratio of energy radiated by P and Q is

Question

Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperature 127° C and 527° C respectively. The ratio of energy radiated by P and Q is (A) 0.054 (B) 0.0034 (C) 1 (D) 2

Tardigrade Admin · Accepted Answer

Total energy radiated from a body Q=Aε 0T4t ⇒ Q propto AT4 propto r2T4 (∵ A=4π r2) ∴ (Qp/QQ)=( (rp/rQ) )2( (Tp/TQ) )4 =( (8/2) )2( (273+127/273+527) )4=1

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

0.054

0.0034

1

2

Total energy radiated from a body
$Q = A ε_{0} T^{4} t$
$\Rightarrow$ $Q \propto A T^{4} \propto r^{2} T^{4}$
$(∵ A = 4 π r^{2})$
$∴$ $\frac{Q _{p}}{Q _{Q}} = (\frac{r _{p}}{r _{Q}})^{2} (\frac{T _{p}}{T _{Q}})^{4}$
$= (\frac{8}{2})^{2} (\frac{273 + 127}{273 + 527})^{4} = 1$

Q. Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperature 127∘C and 527∘C respectively. The ratio of energy radiated by P and Q is

0.054

0.0034

1

2

Total energy radiated from a body Q=Aε0​T4t ⇒ Q∝AT4∝r2T4 (∵A=4πr2) ∴ QQ​Qp​​=(rQ​rp​​)2(TQ​Tp​​)4 =(28​)2(273+527273+127​)4=1

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

Total energy radiated from a body
$Q = A ε_{0} T^{4} t$
$\Rightarrow$ $Q \propto A T^{4} \propto r^{2} T^{4}$
$(∵ A = 4 π r^{2})$
$∴$ $\frac{Q _{p}}{Q _{Q}} = (\frac{r _{p}}{r _{Q}})^{2} (\frac{T _{p}}{T _{Q}})^{4}$
$= (\frac{8}{2})^{2} (\frac{273 + 127}{273 + 527})^{4} = 1$