Question

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

• A. Greater than that by the second
• B. Less than that by the second
• C. Equal in both cases
• D. The information is incomplete to draw any conclusion

Answer 1

Answer: (C)

Equal in both cases

Answer 2

The energy radiated per second E, by a body of surface area A, at temperature TK, is given by

$E = e\sigma AT^{4}$

Hence, $E_{1} = e\sigma 4\pi(1)^{2} \times (4000)^{4}$

$= e\sigma\pi \times 1024 \times 10^{12}Js^{- 1}$And $E_{2} = e\sigma 4\pi(4)^{2}(2000)^{4} = e\sigma\pi \times 1024 \times 10^{12}Js^{- 1}$ So, $E_{1} = E_{2}$