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 `=0.40J^(@)C^(-1)` , thermal conductivity of the material of the rod. `=200Wm^(-1)`^(@)C^(-1)` . Neglect any loss of heat to the atmosphere.

Answer

`12^(@)C//s`

Explanation

`((dT)/(dx))_(A) = 5 ((dT)/(dx)) = 2.6 I = (DeltaT)/(L) (KA)`
`i_(A) = ((dT)/(dx))_(A) KA i_(B) = ((dT)/(dx))_(B) KA`
`I = ((dQ)/(dt))_("Absorb") = [((dT)/(dx))_(A)-((dT)/(dx))_(B)] KA = ms(d theta)/(dt)`
`(5- 2.6) xx 200 xx (1 xx 10^(-2)) = ms (d theta)/(dt)`
`2.4 xx2 = ms (d theta)/(dt) = 4.8`
`ms = 0.4 J//C (d theta)/(dt) = (4.8)/(0.4) = 12^(@)C//s`