For a black-body at absolute temperature T the power emitted per unit area is P. What is the power emitted per unit area when the temperature is decreased to \(\frac{1}{2}\)T?

A. \(\frac{P}{{32}}\)

B. \(\frac{P}{{16}}\)

C. \(\frac{P}{{8}}\)

D. \(\frac{P}{{4}}\)

B