A composite block is made of slabs A,B,C,D and E of different thermal conductivities (given in terms of a constant K and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat 'Q' flows only from left to right through the blocks. Then in steady state

Options

A. heal flow through A and E slabs are same.
B. heat flow through slab E is maximum
C. temperature difference across slab E is smallest.
D. heat flow through C=heat flow through B + heat flow throughD.

Answer

A, C, D

Explanation

(a,c,d)
It is given that heat Q flows only from left to right through
the blocks. Therefore heat flow through A and E slabs are
the same.
`:. [a] is correct option

Since heat flow through slabs A and E is same,
[b] is not correct.
We know that resistance to heat flow is `R=l/(KA)`
Let the width of slabs be Z. Then
`R_A=L/(2K(4L)Z)=1/(8KZ), R_B=(4L)/(3K(LZ))=4/(3KZ)`
`R_C=4L/(4K(2LZ))=1/(2KZ), R_D=(4L)/(5K(LZ))=4/(5KZ)`
`R_E=L/(6K(4LZ))=1/(24KZ)`
Now, `DeltaT=QR`
As `R_E` is least, `DeltaT_E` is also smallest ie since the resistance to
heat flow is least for slab E, the temperature difference across
is smallest.
`:. Option (c) is the correct answer.
Also
`Q_C=(DeltaT_C)/(R_C)=(DeltaT_C)/(1//2KZ)=2KZ(DeltaT_C)
`Q_B=(DeltaT_B)/(R_B)=(DeltaT_C)/(4//3KZ)=(3KZ(DeltaT_C))/4 [:' DeltaT_B=DeltaT_B]`
`Q_D=(DeltaT_D)/(R_D)=(DeltaT_C)/(4//5KZ)=(5KZ(DeltaT_C))/4 [:' DeltaT_D=Delta_C]`
`Q_B+Q_D=(3KZ(DeltaT_C))/4+(5KZ(DeltaT_C))/4`
`=(8KZ(DeltaT_C))/4=2KZ(DeltaT_C)=QC`
`:.` (d) is the correct option.