Which of the following statements is true/correct - Vidyadip

MCQ

Which of the following statements is true/correct

A
During clear nights, the temperature rises steadily upward near the ground level
✓
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 ${S_1}$ 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

Correct option: B.

Newton's law of cooling, an approximate form of Stefan's law, is valid only for natural convection

b
(b) 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 $\frac{Q}{t} = PA\varepsilon \sigma {T^4}$

==> $\frac{{{P_1}}}{{{P_2}}} = \frac{{{A_1}}}{{{A_2}}}.{\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^4} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2}.{\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^4} = {\left( {\frac{1}{4}} \right)^2}\left( {\frac{{4000}}{{200}}} \right) = \frac{1}{1}$
$\because P1 = P2$ , hence option $(d)$ is wrong.

Newton's law is an approximate form of Stefan's law of radiation and works well for natural convection. Hence option $(b)$ is correct.

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