Question

A metal rod of cross sectional area `1.0cm^(2)` is being heated at one end. At one time , the temperature gradient is `5.0^(@)C cm^(-1)` at cross section A and is `2.5^(@)Ccm^(-1)` at cross section B. calculate the rate at which the temperature is increasing in the part AB of the rod. The heat capacity of the part AB`=0.40J^(@)C^(-1)` , thermal conductivity of the material of the rod. `K=200Wm^(-1)C^(-1)` . Neglect any loss of heat to the atmosphere.

Answer 1

Correct Answer - A::B::C
The rate of heat flow per sec
`(dQ_A)/(dt)=KA(d(theta_A))/(dl)`
The rate of heat flow per sec
`(dQ_B)/(dt)=KA(d(theta_B))/(dl)`
the part of heat is absorbed by the rod.,brgt`Q/t=(ms Delta theta)/(dt)`
where `(d theta)/(dt)`= Rate of tempareture variation .
`implies (ms Delta theta)/(dt)=KA(d(theta_A))/(dl)-KA(d(theta_B))/(dl),`
`implies ms(d theta)/(dt)=KA((d(theta_A))/(dl)-(d(theta_B))/(dl))`
`implies0.4(d theta)/(dt)=200xx2.5xx10^(-4)`
`(5-2.5)^(@)C//cm.`
`implies(d theta)/(dt)=(200xx2.5xx10^(-4))/(0.4xx10^(-2))`
`=1250xx10^(-2)=12.50 C/s.`