If a black body emits 0.5 joules of energy per second when it is at 27° C , then the amount of energy emitted by it when it is at 627 °C will be

Question

If a black body emits 0.5 joules of energy per second when it is at 27° C , then the amount of energy emitted by it when it is at 627 °C will be (A) 40.5 J (B) 162 J (C) 13.5 J (D) 135 J

Tardigrade Admin · Accepted Answer

According to Stefan 's law E propto T4 (E1/E2)=[(T1/T2)]4 (E1/0.5)=[(273+627/273+27)]4 E1=0.5((900/300))4 ⇒ E1=40.5 J

Q. If a black body emits $0.5$ joules of energy per second when it is at $2 7^{\circ} C$ , then the amount of energy emitted by it when it is at $627^{\circ}$ C will be

40.5 J

162 J

13.5 J

135 J

According to Stefan 's law
$E \propto T^{4}$
$\frac{E _{1}}{E _{2}} = [\frac{T _{1}}{T _{2}}]^{4}$
$\frac{E _{1}}{0.5} = [\frac{273 + 627}{273 + 27}]^{4}$
$E_{1} = 0.5 (\frac{900}{300})^{4}$
$\Rightarrow E_{1} = 40.5 J$

Q. If a black body emits 0.5 joules of energy per second when it is at 27∘C , then the amount of energy emitted by it when it is at 627∘C will be