Question

A spherical black body with a radius of 12 cm radiates 450W power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be –

• A. 225
• B. 450
• C. 900
• D. 1800

Answer 1

Answer: (D)

1800

Answer 2

P = E/t

E = sT⁴ from unit area, So from, area of radius 12 cm

E' = (s T⁴) [4p(12)²]

$\frac{P'}{P}$ = $\frac{\left\lbrack \sigma(2T)^{4} \right\rbrack\left\lbrack 4\pi\left( \frac{12}{2} \right)^{2} \right\rbrack}{\lbrack\sigma(T)^{4}\rbrack\lbrack 4\pi(12)^{2}\rbrack}$ = 16 × $\frac{1}{4}$ = 4

P' = 450 × 4 = 1800 W