Which of the following statements is true/correct?

Options

A. During clear nights, the temperature rises steadily upward near the ground level
B. Newton's law of colling, an approximate form of Stefan's law, is valid only for natural converction
C. The total energy emitted by a black body per unit time pr unit area is proportional to the square of its temperature in the Kelivin scale
D. Two spheres of the same material have radii 1m 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

B

Explanation

During clear nights object on surface of earth radiate out heat and temperature falls. Hence option (a) is wrong.
The total energy rediated by a body per unit time per unit area `EpropT^(4)`. Hence option (c) is wrong.
Energy radiated per scond is given by
`(Q)/(t)=PAepsisigmaT^(4)`
`implies(P_(1))/(P_(2))=(A_(1))/(A_(2))(T_(1)/(T_(2)))^(4)=((r_(1))/r_(2))^(2).(T_(1)/(T_(2)))^(4)`
`=((1)/(4))^(2)((4000)/(200))=(1)/(1)`
`:'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.