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 $4000K$ and $2000K$ 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
$\frac{Q}{t}=P=A\epsilon \sigma T^4$
$\Rightarrow \frac{P_1}{P_2}=\frac{A_1}{A_2}{\left(\frac{T_1}{T_2}\right)}^4={\left(\frac{r_1}{r_2}\right)}^2.{\left(\frac{T_1}{T_2}\right)}^4$
= ${\left(\frac{1}{4}\right)}^2\left(\frac{4000}{200}\right)=\frac{1}{1}$
$\therefore P_1=P_2,$ hence option (d) is wrong.
Newton's law is an approximate from of Stefan's law of radiation and works well for natural convection.