A spherical black body with a radius of \(12\) cm radiates \(450\) W power at \(500\) K. If the radius were halved and the temperature is doubled, the power radiated in watts would be:
1. \(450\)
2. \(1000\)
3. \(1800\)
4. \(225\)

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t °C, the power received by a unit surface of the earth (normal to the incident rays) at a distance R from the centre of the sun is: 
(where σ is Stefan’s constant.)

1. $\frac{4{\mathrm{\pi r}}^2{\mathrm{\sigma t}}^4}{R^2}$

2. $\frac{r^2\sigma (t+273{)}^4}{4\mathrm{\pi }{R}^2}$

3. $\frac{16{\pi }^2{r}^2{\mathrm{\sigma t}}^4}{R^2}$

4. $\frac{r^2\sigma (t+273{)}^4}{R^2}$

A black body is at 727 °C. It emits energy at a rate that is proportional to:

1. $(727{)}^2$

2. $(1000{)}^4$

3. $(1000{)}^2$

4. $(727{)}^4$

We consider the radiation emitted by the human body. Which of the following statements is true:
 

Which of the following is closest to an ideal black body?