A metal rod of cross-sectional area 1.0 cm 2 is being heated at one end. At one time, the temperature gradient is 5.0°C/cm at cross-section A and is 2.6 °C/cm 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, thermal conductivity of the material of the rod = 200 W/m–°C. Neglect any loss of heat to the atmosphere.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(12 °C/s)
= 5ºC/Cm
= 5, 
= 2.6
i = 
(KA)
i A = 
KA, i B = 
KA
i = 
Absorb = 
KA = ms 
(5 – 2.6) × 200 × (1×10 –2 ) = ms 
2.4 × 2 = ms 
= 4.8
ms = 0.4 J/C
= 
= 12ºC/s
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