A black body radiates energy at the rate of E watt / m 2 at a high temperature T K. When the temperature is reduced to ((T/2)) K, the radiant energy is

Question

A black body radiates energy at the rate of E watt / m 2 at a high temperature T K. When the temperature is reduced to ((T/2)) K, the radiant energy is (A) (E/2) (B) 2 E (C) (E/4) (D) (E/16)

Tardigrade Admin · Accepted Answer

According to Stefan's law, E propto T4 or (E2/E1)=((T2/T1))4 or (E2/E)=((T / 2/T))4=((1/2))4 or E2=(E/16)

Q. A black body radiates energy at the rate of $E$ watt $/ m^{2}$ at a high temperature $T K$ . When the temperature is reduced to $(\frac{T}{2}) K$ , the radiant energy is

$\frac{E}{2}$

$2 E$

$\frac{E}{4}$

$\frac{E}{16}$

According to Stefan's law,
$E \propto T^{4}$
or $\frac{E _{2}}{E _{1}} = (\frac{T _{2}}{T _{1}})^{4}$
or $\frac{E _{2}}{E} = (\frac{T /2}{T})^{4} = (\frac{1}{2})^{4}$
or $E_{2} = \frac{E}{16}$

Q. A black body radiates energy at the rate of E watt /m2 at a high temperature TK. When the temperature is reduced to (2T​)K, the radiant energy is

2E​

2E

4E​

16E​