$A$ black body radiates heat energy at the rate of $2 \times 10^5 \, J/s \cdot m^2$ at a temperature of $127 \, ^\circ C$. The temperature of the black body at which the rate becomes $32 \times 10^5 \, J/s \cdot m^2$ is ....... $^\circ C$.

$A$ black sphere has radius $R$ whose rate of radiation is $E$ at temperature $T$. If the radius is made $R/2$ and the temperature $3T$,the rate of radiation will be:

$A$ body emits $5 \ W$ of energy at a temperature of $127^{\circ}C$. If the temperature is increased to $927^{\circ}C$,then the emitted energy becomes .......... $W$.

$A$ tungsten body of diameter $2.3 \ cm$ is at $2000 \ ^oC$. It radiates $30 \%$ of the energy radiated by a black body of the same radius and temperature. Find the radius of a black body which will radiate energy at the same rate at the same temperature (in $cm$).

The rate of radiation by a black body is $R$ at temperature $T$. Another body has the same area but an emissivity of $0.2$ and a temperature of $3T$. Its rate of radiation is: (in $R$)

$A$ solid cylinder of radius $r_1=2.5 \ cm$,length $l_1=5.0 \ cm$ and temperature $40^{\circ}C$ is suspended in an environment of temperature $60^{\circ}C$. The thermal radiation transfer rate for the cylinder is $1.0 \ W$. If the cylinder is stretched until its radius becomes $r_2=0.50 \ cm$,the thermal radiation transfer rate is changed to (in $W$)