The power received at distance d from a small metallic sphere of radius r(

Question

The power received at distance d from a small metallic sphere of radius r(<< d ) and at absolute temperature T is P. If temperature is doubled and distance reduced to half of initial value, then the power received at that point will be (A) 4p (B) 8p (C) 32p (D) 64p

Tardigrade Admin · Accepted Answer

Solar constant propto (T4/r2) Solar constant equivalent to power received so (P1/P2)=(T14/r12) × (r22/T24) (P/P2)=(T4/r2) × ((r / 2)2/(2 T)4) P2=64 p

Q. The power received at distance $d$ from a small metallic sphere of radius $r (<< d$ ) and at absolute temperature $T$ is $P$ . If temperature is doubled and distance reduced to half of initial value, then the power received at that point will be

4p

8p

32p

64p

Solar constant $\propto \frac{T ^{4}}{r ^{2}}$
Solar constant equivalent to power received so
$\frac{P _{1}}{P _{2}} = \frac{T _{1}^{4}}{r _{1}^{2}} \times \frac{r _{2}^{2}}{T _{2}^{4}}$
$\frac{P}{P _{2}} = \frac{T ^{4}}{r ^{2}} \times \frac{( r /2 ) ^{2}}{( 2 T ) ^{4}}$
$P_{2} = 64 p$

Q. The power received at distance d from a small metallic sphere of radius r(<<d ) and at absolute temperature T is P. If temperature is doubled and distance reduced to half of initial value, then the power received at that point will be

4p

8p

32p

64p

Solar constant ∝r2T4​ Solar constant equivalent to power received so P2​P1​​=r12​T14​​×T24​r22​​ P2​P​=r2T4​×(2T)4(r/2)2​ P2​=64p

Q. The power received at distance $d$ from a small metallic sphere of radius $r (<< d$ ) and at absolute temperature $T$ is $P$ . If temperature is doubled and distance reduced to half of initial value, then the power received at that point will be

Solar constant $\propto \frac{T ^{4}}{r ^{2}}$
Solar constant equivalent to power received so
$\frac{P _{1}}{P _{2}} = \frac{T _{1}^{4}}{r _{1}^{2}} \times \frac{r _{2}^{2}}{T _{2}^{4}}$
$\frac{P}{P _{2}} = \frac{T ^{4}}{r ^{2}} \times \frac{( r /2 ) ^{2}}{( 2 T ) ^{4}}$
$P_{2} = 64 p$