Question

A copper rod 2 m long has a circular cross-section of radius 1 cm. One end is kept at 100^@C and the other at 0^@C. The surface is insulated so that negligible heat is lost through the surface. In steady state, find (a) the thermal resistance of the bar (b) the thermal current H (c) the temperature gradient (dT)/(dx) and (d) the temperature at a distance 25 cm from the hot end. Thermal conductivity of copper is 401 W//m-K.

Answer 1

Given :

Length =  2m

cross-section = 1cm

Temperature at one end =100°C

Temperature at another end = 0°C

To find:

a)Thermal resistance of the bar

b)Thermal current H

c)Temperature gradient

d)Temperature

Solution :

• a)Thermal resistance “R=l/KA”

            R=l/(πr²×K) = 15.9 K/W

           Thermal Resistance of the bar=15.9 K/W

• b) H = Δ∅/R

           H = 100 - 0/15.9 = 6.3W

           Thermal current H = 6.3 W

• c) temperature gradient= (0-100)/2

                                       =-50C/m

           temperature gradient is -50C/m

• d)∅ be the temperature at a distance of 25 cm From hot end

         ∅-100 = Temperature gradient ×distance

         ∅-100 = -50×0.25

         ∅=87.5°C

       

Answer 2

Answer:

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