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Q.

A rod of length l and cross-sectional area A has a variable conductivity given by K = αT, where α is a positive constant and T is temperature in kelvin. Two ends of the rod are maintained at temperatures T1 and T2 T1>T2. Heat current flowing through the rod will be

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a

AαT12−T22l

b

AαT12+T22l

c

AαT12+T223l

d

AαT12−T222l

answer is D.

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Detailed Solution

Heat current:i=−kAdTdxidx=−kAdTi∫0l dx=−Aα∫T1T2 TdTil=−AαT22−T122⇒i=AαT12−T222l
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A rod of length l and cross-sectional area A has a variable conductivity given by K = αT, where α is a positive constant and T is temperature in kelvin. Two ends of the rod are maintained at temperatures T1 and T2 T1>T2. Heat current flowing through the rod will be