A rectangular block of surface area A emits energy E per second at $27^{\circ} \mathrm{C}$. If length and breadth is reduced to half of initial value and temperature is raised to $327^{\circ} \mathrm{C}$ then energy emitted per second becomes

The Stefan-Boltzmann Law $E = \epsilon \sigma A T^4$ relates the energy radiated per second to surface area and temperature. Given the initial conditions $A_1 = A$ and $T_1 = 300\, \mathrm{K}$, the energy emitted is $E_1 = E$.

When the length and breadth are halved, the surface area becomes $A_2 = A/4$. The temperature is $T_2 = 600\, \mathrm{K}$. The ratio of energies is

$\frac{E_2}{E_1} = \frac{A_2}{A_1} \left( \frac{T_2}{T_1} \right)^4 = \frac{1}{4} \times 2^4 = 4$.

The energy emitted per second becomes $4E$.