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A Metal Rod of Cross Sectional Area 1.0 Cm2 is Being Heated at One End. at One Time, the Temperatures Gradient is 5.0°C Cm−1 at Cross Section a and is 2.5°C Cm−1 - Physics

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Question

A metal rod of cross sectional area 1.0 cm2 is being heated at one end. At one time, the temperatures gradient is 5.0°C cm−1 at cross section A and is 2.5°C cm−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 = 0.40 J°C−1, thermal conductivity of the material of the rod = 200 W m−1°C−1. Neglect any loss of heat to the atmosphere

Solution

Let the temperatur
Let the temperatures at the ends A and B be TA and TB, respectively.

Rate of flow of heat at end A of the rod is given by

`(dQ_A)/(dr)= KA. d/dt (T_A)`

Rate of flow of heat at end B of the rod is given by

`(dQ_B)/dt ( T_B)`

Heat absorbed by the rod = ms∆T
Here, s is the specific heat of the rod and ∆T is the temperature difference between ends A and B.

Rate of heat absorption by the rod is given by

`(dQ)/dt =ms (dT)/(dr)`

∴ ` ms (dT)/(dr)=  (KA. dT_A
)/(dl)`

`⇒ (0.4). (dT)/ dt= 200 xx 1xx 10^-4xx (5-2.5) `

`dt/dr=12.5^circ` C/sec

  Is there an error in this question or solution?

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Solution A Metal Rod of Cross Sectional Area 1.0 Cm2 is Being Heated at One End. at One Time, the Temperatures Gradient is 5.0°C Cm−1 at Cross Section a and is 2.5°C Cm−1 Concept: Thermal Expansion of Solids.
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