$A$ black body at temperature $127^{\circ} C$ radiates heat at the rate of $5 \ cal / cm^2 \ s$. At a temperature $927^{\circ} C$,its rate of emission in units of $cal / cm^2 \ s$ will be

At $127^{\circ}C$,the radiated energy is $2.7 \times 10^{-3} \text{ J/s}$. At what temperature in $K$ is the radiated energy $4.32 \times 10^{6} \text{ J/s}$?

$A$ thin steel square plate of side $10 \ cm$ is heated. The rate of energy emission from the heated plate is $1134 \ W$. What is the temperature of the plate in $K$? (Assume emissivity $\varepsilon = 1$ and $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

$A$ spherical black body of radius $r$ radiates power $P$ and its rate of cooling is $R$. Which of the following relations are correct?
$(i) \ P \propto r$
$(ii) \ P \propto r^2$
$(iii) \ R \propto r^2$
$(iv) \ R \propto \frac{1}{r}$

The temperature of a black body is increased by $50 \%$. The percentage increase in the rate of radiation by the body is approximately: (in $\%$)

Two spheres of the same material have radii $1 \; m$ and $4 \; m$ and temperatures $4000 \; K$ and $2000 \; K$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is