A rod of unifrom cross section is heated at temperature `t_(0)` at a point which is at `n_(1)` times if its length `(n_(1) lt 1)` from its one end in stready state The temperature at this end is `t_(1)` and at other end is `t_(2)` Rate of vapourisation of water at either end of the rod is same. The end at which temperature is `t_(2)` is how much more far away that the other end from the point at which the rod is heated .

Options

A. `(n_(1)(t_(0)-t_(2)))/(t_(0)-t_(1))`
B. `(n_(1)(t_(0)-t_(2)))/(t_(0)-t_(1))`
C. `(2n_(1)t_(0))/(t_(0)-t_(2))`
D. `(2n_(1)(t_(1)-t_(2)))/(t_(0)-t_(1))`

Answer

D

Explanation

`(dQ)/(dt)=L(dm)/(dt),(dm)/(dt)=(KA)/(l).(DeltaT)/(L),((dm)/(dt))_(1)=((dm)/(dt))_(2)`
`(t_(0)-t_(1))/(n_(1)lL)=(t_(0)-t_(2))/(n_(2)lL),(n_(2))/(n_(1))= (t_(0)-t_(2))/(t_(0)-t_(1))`
`(n_(2)-t_(1))/(n_(1))=(Deltan)/(n_(1))=(t_(1)-t_(2))/(t_(0)-t_(1))`
`(n_(2)-n_(1))/(n_(1))=(Deltan)/(n_(1))=(t_(1)-t_(2))/(t_(0)-t_(1))` .