Question

A solid cube of edge length r, a solid sphere of radius r, and a solid hemisphere of radius r, all made of the same material, are maintained at temperature 300 K in an environment at temperature 350 K. Rank the objects according to the net rate at which thermal radiation is exchanged with the environment, greatest first.

Answer 1

Answer:

Explanation:

The rate at which heat will be radiated is given by the expression

E = e Aσ ( T⁴ - T₀⁴ )

E is heat radiated , e is emissivity , A is area of surface , σ  is stephan's constant T is temperature of the object and T₀ is temperature of the surrounding .

For all the objects given , e , σ T and T₀ are same so E will solely dependent on area of the surface

surface area of cube= 6 r² ,

surface area of sphere = 4 π r²

= 12.56 r²

hemisphere = 2 π r²

= 6.28 r²

12.56 r² >6.28 r² > 6 r²

heat radiated by sphere > heat radiated by hemisphere > heat radiated by cube .