Question

Which of the following statements is true/correct ?

• A. During clear nights, the temperature rises steadily upward near the ground level
• B. Newton’s law of cooling, an approximate form of Stefan’s law, is valid only for natural convection
• C. The total energy emitted by a black body per unit time per unit area is proportional to the square of its temperature in the Kelvin scale
• D. Two spheres of the same material have radii $ 1m $ and $ 4m $ and temperatures $ 4000\,K $ and $ 2000\, K $ respectively. The energy radiated per second by the first sphere is greater than that radiated per second by the second sphere

Answer 1

Answer: (B)

Energy radiated per second is given by
$ \frac{Q}{t}=P=A\varepsilon\sigma T^4 $
$ \Rightarrow \frac{P_1}{P_2}=\frac{A_1}{A_2}\left(\frac{T_1}{T_2}\right)^4=\left(\frac{r_1}{r_2}\right)^2.\left(\frac{T_1}{T_2}\right)^4 $
= $ \left(\frac{1}{4}\right)^2\left(\frac{4000}{200}\right)=\frac{1}{1} $
$ \therefore P_1 = P_2, $ hence option (d) is wrong.
Newton's law is an approximate from of Stefan's law of radiation and works well for natural convection.