The heat radiated per unit area in $1\,hour$ by a furnace whose temperature is $3000\,K$ is $(\sigma = 5.7 \times 10^{-8}\,W\,m^{-2}\,K^{-4})$.

Two electric lamps $A$ and $B$ radiate the same power. Their filaments have the same dimensions and have emissivities $e_A$ and $e_B$. Their surface temperatures are $T_A$ and $T_B$. The ratio $\frac{T_A}{T_B}$ will be equal to :-

$A$ star $(P)$ behaves like a perfectly black body emitting radiant energy at temperature $T$. Another star $(Q)$ also behaves like a perfectly black body emitting radiant energy at temperature $T/4$ and has a radius eight times the radius of star $(P)$. The ratio of radiant energy emitted by $(P)$ to that by $(Q)$ is

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

$A$ black body at a temperature of $127^{\circ}C$ radiates heat at the rate of $1 \ cal/cm^2 \cdot s$. At a temperature of $527^{\circ}C$,the rate of heat radiation from the body in $cal/cm^2 \cdot s$ will be:

The total energy of a black body radiation source is collected for five minutes and used to heat water. The temperature of the water increases from $10.0^{\circ} C$ to $11.0^{\circ} C$. The absolute temperature of the black body is doubled and its surface area halved and the experiment repeated for the same time. Which of the following statements would be most nearly correct?