The left end of a copper rod (length=`20cm`, Area of cross section=`0.2cm^(2)`) is maintained at `20^(@)C` and the right end is maintained at `80^(@)C` . Neglecting any loss of heat through radiation, find (a) the temperature at a point 11cm from the left end and (b) the heat current through the rod. thermal conductivity of copper `=385Wm^(-1)C^(-1)` .

Answer

A, B, C

Explanation

`l=20cm=20xx10^(-2) m,`
`A=0.2 cm^(2)=0.2xx10^(-4) m^(2)`
`T_(1)=80^(@)C` `T_(2)=20^(@)C`,brgt`k=385`
(a) `Q/t=(kA(T_1-T_2))/(l)`
`=(385xx0.2xx10^(-4)(80-20))/(20xx10^(-2))`
`(385xx2xx10^(-5)XX60)/(20XX10^(-2))`
`=385xx6xx10^(-4)xx10`
`=2319xx10^(-3)=2.31 J//s.`
(b)Let the temperature of the 1 point at 11 cm be T.
`(Delta T)/l=(Q)/tkA.`
`implies (Delta t)/l=2.31/(385xx0.2xx10^(-4))`
`implies (T=20)/(11xx10^(-2))=2.31/(385xx0.2)xx10^(-4)`
`implies T=20=(2.31xx10^(-4))/(385xx0.2)xx11xx10^(-2)`
`=33`
`implies T=33+20=53^(@)C.`