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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 :

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 .

batolisis

Ranking the objects based on the net rate by which thermal radiation occurs

  • Sphere ( 12.56 r² ) > Hemisphere ( 6.28 r² )   > Cube ( 6r² )

The net rate of thermal radiation is expressed as

E = e*A*∝ ( T₁⁴ - T₀⁴ ) ----- ( 1 )

where : e = emissivity , A = Area of object ,  ∝ = stephen constant, T₁ = object temperature , T₀ = temperature of surroundings.

From the question the values of   e, T and ∝  are constant

Determine the net rate of thermal radiation ( E ) for each object

E = A --- ( 2 )

  • For solid cube

       E =  A = 6r²

  • For sphere

       E= A = 4πr² = 12.56 r²

  • For Hemisphere

       E= A = 2πr² = 6.28 r²

Hence ranking the objects based on their thermal radiation,Sphere ( 12.56 r² ) > Hemisphere ( 6.28 r² )   > Cube ( 6r² )

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