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Which of the following statements is true/correct
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
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
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
Solution
(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.
