Heat conduction through a thick spherical shell: select the correct steady-state formula. Let inner radius = r1, outer radius = r2, thermal conductivity = k, inner and outer surface temperatures = T1 and T2 respectively (T1 > T2). Choose the correct expression for the total heat flow rate Q (steady, 1-D radial conduction).

Concept/ApproachSteady 1-D radial conduction in a sphere gives a thermal resistance R_th = (1/(4πk))·(1/r1 − 1/r2). Hence Q = ΔT/R_th.

Step-by-stepR_th = (1/(4πk))·(1/r1 − 1/r2)Q = (T1 − T2) / R_th = 4πk (T1 − T2) / (1/r1 − 1/r2)Equivalent form: Q = 4πk r1 r2 (T1 − T2)/(r2 − r1)

Option checkA matches the standard spherical formula (correct).B is for a cylinder of length L (not a sphere).C assumes planar 1-D conduction with area A (not applicable here).D is an equivalent correct form numerically; however the problem statement requests selection of one expression—A is the canonical spherical resistance form.

Final AnswerQ = 4πk (T1 − T2) / (1/r1 − 1/r2).