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A long rod has one end at 0^@C and other...

A long rod has one end at `0^@C` and other end at a high temperature. The coefficient of thermal conductivity varies with distance from the low temperature end as `K = K_0(1+ax)`, where `K_0 = 10^2` SI unit and `a = 1m^-1` . At what distance from the first end the temperature will be `100^@C`? The area of cross-section is `1cm^2` and rate of heat conduction is 1 W.

A

2.7 m

B

1.7m

C

3 m

D

1.5 m

Text Solution

Verified by Experts

The correct Answer is:
B
`H = (TD)/R`
`:. R = (TD)/H = (100 -0)/1`
`=100kW^-1`
Now, `R= int_(0)^x dR = int_(0)^x ((dx)/(K_0(1+ax)A))`
or `100 = int_(0)^x (dx)/(10^2(1+x)(10^-4))`
Solving this equation we get,
`x = 1.7 m.`
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