A copper rod (initially at room temperature `20^(@)C`) of non-uniform cross section is placed between a steam chamber at `100^(@)C` and ice-water chamber at `0^(@)C`. `A` and `B` are cross sections are as shown in figure. Then match the statements in column -I with results in columns-II using comparing only between cross section `A` and `B`. (The mathematical expressions in column-I have usual meaning in heat transfer).

`{:(,"Column-I",,"Column-II"),((A),"initially rate of heat flow" ((dQ)/(dt))"will be ",(p),"Maximum at section" A),((B),"At steady state rate of heat flow" ((dQ)/(dt)) "will be ",(q),"Maximum at section" B),((C),"At steady state temperature gradient" |((dT)/(dx))| "will be " ,(r),"Minimum at section B"), ((D), "At steady state rate of change of temperature"((dT)/(dt)) " at a certain point will be",(s),"Same for all section"):}`

Answer

A-P,R;B-S;C-Q;D-S

Explanation

Initially, both temperature and area is more at A. So, the rate of flow of heat is maximum at A. At steady state, rate of heat flow is constant for all cross sections.
As `(dQ)/(dt)=KA(-(dT)/(dx))rArr|(dT)/(dx)|prop(1)/(A)`
At steady state, T is constant for every cross section. Hence, `(dT)/(dt)=0` at steady state.