A sphere of $$3$$ cm radius acts like a black body. If it is in equilibrium with its surroundings and absorb $$30$$ k watt of energy radiated to it from the surrounding. Then the temperature of the sphere will be

Question

Infinity Learn · Accepted Answer

Radius of sphere r $$=$$ $$3$$ cm $$=$$ $$0.03$$ m The energy absorbed  E $$=$$ $$30$$ kW $$=$$ $$30$$ × $$103$$ wattEnergy absorbed by black body when the temperature of surroundings is T, is given byE $$=$$ σ$$AT4or$$ $$30$$ × $$103$$ $$=$$ $$5.672$$ ×$$10-8$$×$$4$$π$$(0.03)2$$×$$T4$$     $$30$$ × $$103$$ $$=$$ $$0.64$$ ×$$10-8$$×$$T4$$      $$T4$$ $$=$$ $$30$$×$$1030.064$$×$$10-8$$ $$=$$ $$46.875$$ ×$$1012$$        $$=$$ $$2.616$$ ×  $$103$$ $$=$$ $$2616$$ K

A sphere of 3 cm radius acts like a black body. If it is in equilibrium with its surroundings and absorb 30 k watt of energy radiated to it from the surrounding. Then the temperature of the sphere will be

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material