Entries in column I consists of diagrams of thermal conductors. The type of conductor & direction of heat flows are listed below. Entries in column II consists of the magnitude of rate of heat flow belonging to any of the entries in column I. If temperature difference in all the cases is (T1 – T2), then match columnColumn IColumn II(P) (1) 6πk0R(T1 – T2)(Q) (2) (R) (3) πk0R(T1

Engineering

Physics

Conduction of Heat

Question

Entries in column I consists of diagrams of thermal conductors. The type of conductor & direction of heat flows are listed below. Entries in column II consists of the magnitude of rate of heat flow belonging to any of the entries in column I. If temperature difference in all the cases is (T₁ – T₂), then match column

Column I	Column II
(P)	(1) 6πk₀R(T₁ – T₂)
(Q)	(2) $\frac{{πk}_{0} R}{3 \ln 2} (T_{1} - T_{2})$
(R)	(3) πk₀R(T₁ – T₂)
(S)	(4) $\frac{4 {πk}_{0} R}{\ln 2} (T_{1} - T_{2})$

P-3, Q-1, R-4, S-2

P-3, Q-2, R-4, S-1

P-4, Q-3, R-2, S-1

P-1, Q-2, R-3, S-4

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$(A) \frac{ΔQ}{Δt} = \frac{k_{0} [π {(2 R)}^{2} - {πR}^{2}]}{3 R} (T_{1} - T_{2}) = {πRk}_{0} (T_{1} - T_{2})$

$(B) \frac{ΔQ}{Δt} = \frac{4 {πkR}_{1} R_{2}}{(R_{2} - R_{1})} (T_{1} - T_{2}) = \frac{4 {πk}_{0} 3 R \cdot R}{(3 R - R)} (T_{1} - T_{2}) = 6 {πk}_{0} R (T_{1} - T_{2})$

$(C) \frac{ΔQ}{Δt} = \frac{2 {πk}_{0} l}{l n (\frac{R_{2}}{R_{1}})} (T_{1} - T_{2}) = \frac{4 {πk}_{0} R}{\ln 2} (T_{1} - T_{2})$

$(D) \frac{ΔQ}{Δt} = - π R^{2} k· \frac{dT}{dx} = - π R^{2} k_{0} (1 + \frac{x}{3 R}) \frac{dT}{dx}$

$∴ \frac{ΔQ}{Δt} = \int_{0}^{3 R} \frac{dx}{(1 + \frac{x}{3 R})} = - {πR}^{2} k_{0} \int_{T_{1}}^{T_{2}} dt$

$\frac{ΔQ}{Δt} = {\frac{\ln (1 + \frac{x}{3 R})}{(R / 3)} |}_{0}^{3 R} = {πR}^{2} k_{0} (T_{1} - T_{2})$

$∴ \frac{ΔQ}{Δt} = \frac{{πk}_{0} R (T_{1} - T_{2})}{3 \ln 2}$