The power radiated by a perfect black body is thought to depend only on its surface area

PHYSICS · Single correct · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

The power

P

radiated by a perfect black body is thought to depend only on its surface area

A

, absolute temperature

\theta

and the Stefan constant

\sigma

. Which proportionality is permitted by dimensional analysis? (Here

C

is a dimensionless constant.) (a)

P = C\,\sigma A^{2}\theta^{4}

(b)

P = C\,\dfrac{\sigma \theta^{4}}{A}

(c)

P = C\,\sigma A \theta^{4}

(d)

P = C\,\sigma A \theta^{2}