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 mB. 1.7mC. 3 mD. 1.5 m

A long rod has one end at `0^@C` and other end at a high temperature.

1.	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 mB. 1.7mC. 3 mD. 1.5 m
Answer» Correct Answer - B<br>`H = (TD)/R`<br> `:. R = (TD)/H = (100 -0)/1`<br> `=100kW^-1`<br> Now, `R= int_(0)^x dR = int_(0)^x ((dx)/(K_0(1+ax)A))`<br> or `100 = int_(0)^x (dx)/(10^2(1+x)(10^-4))`<br> Solving this equation we get,<br> `x = 1.7 m.`

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