The figure shows a system of two concentric spheres of radii ${r}_{1}$ and ${r}_{2}$ and kept at temperatures ${T}_{1}$ and ${T}_{2}$ , respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Question

The figure shows a system of two concentric spheres of radii

{r}_{1}

and

{r}_{2}

and kept at temperatures

{T}_{1}

and

{T}_{2}

, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

The figure shows a system of two concentric spheres of radii r _ 1 and r _ 2 and kept at temperatures T _ 1 and T _ 2 ,

Quantrex Academy · Accepted Answer

Correct answer: A. r _ 1 r _ 2 ( r _ 2 - r _ 1 )

For conduction from inner sphere to outer one, dQ = - KA dT dr × (time dt) or~ and and and dQ dt = - K × (4 ^ 2 ) dT dr ∴ Radial rate of flow dQ dt =P = - 4 ^ 2 (dT)/(dr) ∴ ~ & & P ∫ _ r1 ^ r2 dr r2 = -4 ∫ _ T1 ^ T2 dT or P [ r _ 1 - r _ 2 r _ 1 r _ 2 ] =4 [ T _ 2 - T _ 1 ] or P = 4 ( T _ 1 - T _ 2 ) r _ 1 r _ 2 ( r _ 2 - r _ 1 ) ∴ ~ dQ dt is proportional to ( r _ 1 r _ 2 r _ 2 - r _ 1 ) .

The figure shows a system of two concentric spheres of radii r _ 1...

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