Question

If a body coated black at 600 k surrounded by atmosphere at, 300 k has cooling rate $r_1$ the same body at 900 k surrounded by the same atmosphere , will have cooling rate equal to

• A. $\frac{16}{3}{r}_1$
• B. $\frac{8}{16}{r}_0$
• C. $16r_0$
• D. $4r_0$

Answer 1

The correct option is A $\frac{16}{3}{r}_1$

Rate of cooling

$r\propto T^4-T_0^4$

$\frac{r_2}{r_1}\Rightarrow \frac{(900{)}^4-(300{)}^4}{(600{)}^4-(300{)}^4}$

$\Rightarrow \frac{9^4-3^4}{6^4-3^4}\Rightarrow \frac{{81}^2-9^2}{{36}^2-9^2}$

$\frac{r_2}{r_1}\Rightarrow \frac{16}{3}$