A rod of length l with thermally insulated lateral surface is made of a matrical whose thermal conductivity varies as `K =C//T` where `C` is a constant The ends are kept at temperature `T_(1)` and `T_(2)` The temperature at a distance x from the first end where the temperature is `T_(1), T =T_(1)((T_(2))/(T_(1)))^(nx//2l)` Find the value of n? .

Answer

B

Explanation

`(dQ)/(dt)=(CAdT)/(Tdx),(dQ)/(dt)underset(0)overset(x)intdx=CAunderset(T_(i))overset(T)int(dT)/(T)`
`(dQ)/(dt)x=cAIn(T)/T_(1),(i)(dQ)/dtl=CAIn(T_(2))/(T_(1))`
`(x)/(l)=In(T//T_(1))/(T_(2)//T_(1)),T=T_(1)((T_(2))/(T_(1)))^(x//l)`
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