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 $1 m$ and $4 m$ 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 1

Answer: (B)

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

Answer 2

During clear nights object on surface of earth radiate out heat and temperature falls. Hence option (1) is wrong. The total energy radiated by a body per unit time per unit area E ∝ T⁴. Hence option (3) is wrong.

Energy radiated per second is given by $\frac { Q } { t } = P A \varepsilon \sigma T ^ { 4 }$

⇒ $\frac { P _ { 1 } } { P _ { 2 } } = \frac { A _ { 1 } } { A _ { 2 } } \cdot \left( \frac { T _ { 1 } } { T _ { 2 } } \right) ^ { 4 } = \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 2 } \cdot \left( \frac { T _ { 1 } } { T _ { 2 } } \right) ^ { 4 } = \left( \frac { 1 } { 4 } \right) ^ { 2 } \left( \frac { 4000 } { 200 } \right) = \frac { 1 } { 1 }$

P₁ = P₂, hence option (4) is wrong.

Newton's law is an approximate form of Stefan's law of radiation and works well for natural convection. Hence option (2) is correct.