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, and 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

The correct option is B Newton's law of cooling, and approximate form of Stefan's law, is valid only for natural convection

During clear nights object on surface of earth radiate out heat and temperature falls. Hence option (a) is wrong.
The total energy radiated by a body per unit time per unit area $E\propto T^4$. Hence option (c) is wrong.
Energy radiated per second is given by
$\frac{Q}{t}=PA\epsilon \sigma T^4$
$\Rightarrow \frac{P_1}{P_2}=\frac{A_1}{A_2}{\left(\frac{T_1}{T_2}\right)}^4={\left(\frac{r_1}{r_2}\right)}^2\cdot {\left(\frac{T_1}{T_2}\right)}^2$
$={\left(\frac{1}{4}\right)}^2\left(\frac{4000}{200}\right)=\frac{1}{1}$
$\because P_1=P_2$ hence option (d) is wrong.
Newton's law is an approximate from of Stefan's law of radiation and works well for natural convection. Hence option (b) is correct.