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A cylinder of radius R, made of a material of thermal 
conductivity 
, is surrounded by a cylindrical shell 
of inner radius R and outer radius 2R. The shell is 
made of a material of thermal conductivity 
. The 
two different 
temperatures
. There is no loss of heat 
across the cylindrical surface and the system is in 
steady state. The effective thermal conductivity of 
the system is
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A cylinder of radius R, made of a material of thermalconductivity,is s...
The answer is c.
Let the difference between the temperatures across the two ends be ΔT length of the cylinder be L.
Let ΔH1 and ΔH2 is the heat transferred by the inner and outer conductor in time Δt.
Heat transferred by inner cylinder in time Δt is given
ΔH1/ Δt = (K1πR2 ΔT)/L
=> ΔH1 = (K1πR2 ΔT)Δt/L  ---1
Heat transferred by outer cylinder in time Δt is given
ΔH2/ Δt = (K2π{(2R)2 – R2 }ΔT)/L
=> ΔH2 = (3K2πR2 ΔT)Δt/L  ---2
Total heat transferred
ΔH = ΔH1 + ΔH2
From eqn. 1 and 2
ΔH  = (K1πR2 ΔT)Δt/L  +  (3K2πR2 ΔT)Δt/L
=> ΔH/ Δt = (K1 + 3K2)πR2/L
Now the total radius of the system R’ = 2R
ΔH/ Δt = (K1 + 3K2)π(2R)2/4L
             = (K1 + 3K2)π(R’)2/4L
             = 1/4(K1 + 3K2) π(R’)2/L
             = K π(R’)2/L
K = equivalent thermal conductivity
K = 1/4(K1 + 3K2)
This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
A cylinder of radius R, made of a material of thermalconductivity,is s...
R1 = Initial radius = R & R2 = final radius = 2R
  The two conductors are thermally in parallel. Therefore, equivalent thermal resistance R is given by:-
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A cylinder of radius R, made of a material of thermalconductivity,is surrounded by a cylindrical shellof inner radius R and outer radius 2R. The shell ismade of a material of thermal conductivity.Thetwo differenttemperatures. There is no loss of heatacross the cylindrical surface and the system is insteady state. The effective thermal conductivity ofthe system is a) b) c) d) Correct answer is option 'B'. Can you explain this answer?
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