Answer

Verified

79.8k+ views

**Hint:**Amount of heat radiated by tungsten will be equal to the amount of energy supplied. According to Stephan’s law the heat loss is given by, \[e\sigma A({T^2} - {T_0}^2)\] . Substitute the values of initial and final temperature, area, emissivity and the constant. Simplify to find the value power required.

**Complete step-by-step solution**

Energy is never produced or destroyed in this universe; there is always a transfer of energy from one form to another. Energy loss can be in the form of heat. In our case also, the amount of heat to be supplied per unit time to maintain the temperature of the sphere is the heat lost per unit time by that sphere.

Using Stephan’s law,

\[

Heat\,lost\,of\,radiation = e\sigma A({T^2} - {T_0}^2) \\

T = 3000k \\

{T_0} = 300k \\

A = 4\pi {r^2} = 4\pi \times {0.01^2} \\

Substituting, \\

P = 0.35 \times 5.67 \times {10^{ - 8}} \times 4\pi {(0.01)^2}[{3000^2} - {300^2}] \\

P = 2019.8W \\

\]

**Therefore, the correct answer is option B.**

**Note:**This equation is in terms of power or heat transferred per unit time. If you want to calculate the heat transferred in say 1 minute, then multiply the power value with 60s.According to Stephan's law the radiant energy emitted by a perfectly black body per unit area per second is directly proportional to the fourth power of its absolute temperature.

$E \propto {T^4} \Rightarrow E = \sigma {T^4}$

Recently Updated Pages

Name the scale on which the destructive energy of an class 11 physics JEE_Main

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main