Entries in List-I consist of diagrams of thermal conductors. The type of conductor and direction of heat flow are listed below. Entries in List-II consist of the magnitude of rate of heat flow belongi

Question

Entries in List-I consist of diagrams of thermal conductors. The type of conductor and direction of heat flow are listed below. Entries in List-II consist of the magnitude of rate of heat flow belonging to any of the entries in List-I. If temperature difference in all the cases is $(T_{1} - T_{2})$ , then match the lists. (List-I figures: I = hollow cylinder, axial flow, length $3 R$ , radii $R$ and $2 R$ ; II = thick spherical shell, radii $R$ and $3 R$ , radial flow; III = thick cylindrical shell, length $2 R$ , radii $R$ and $2 R$ , radial flow; IV = solid cylinder, radius $R$ , length $3 R$ , axial flow.)

List - I	List - II
(I) figure I	(P) $6 π k_{0} R (T_{1} - T_{2})$
(II) figure II (thick spherical shell, radial flow)	(Q) $\frac{π k _{0} R}{3} (T_{1} - T_{2})$
(III) figure III (thick cylindrical shell, radial flow)	(R) $π k_{0} R (T_{1} - T_{2})$
(IV) figure IV	(S) $\frac{4 π k _{0} R}{ln 2} (T_{1} - T_{2})$
	(T) None

TestHub · Accepted Answer

(I) Axial flow, area π [( 2 R ) 2 − R 2 ] = 3 π R 2 , length 3 R : d t d Q ​ = 3 R k 0 ​ ( 3 π R 2 ) Δ T ​ = π k 0 ​ R Δ T → R. (II) Spherical shell: d t d Q ​ = r 2 ​ − r 1 ​ 4 π k 0 ​ r 1 ​ r 2 ​ Δ T ​ = 2 R 4 π k 0 ​ ( R ) ( 3 R ) ​ Δ T = 6 π k 0 ​ R Δ T → P. (III) Cylindrical shell: d t d Q ​ = ln ( r 2 ​ / r 1 ​ ) 2 π k 0 ​ L Δ T ​ = ln 2 2 π k 0 ​ ( 2 R ) Δ T ​ = ln 2 4 π k 0 ​ R ​ Δ T → S. (IV) Solid cylinder: 3 R k 0 ​ ( π R 2 ) Δ T ​ = 3 π k 0 ​ R ​ Δ T → Q. I → R, II → P, III → S, IV → Q: option (B).

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