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QPages 98-102: Q18: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q18 Solution: A metal rod of cross sectional area is being heated at one end. …

A metal rod of cross sectional area

1.0 \text{ cm}^2

is being heated at one end. At one time, the temperature gradient is

5.0 \text{ �C cm}^{-1}

at cross section A and is

2.5 \text{ �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 \text{ J �C}^{-1}

, thermal conductivity of the material of the rod =

200 \text{ W m}^{-1} \text{ �C}^{-1}

. Neglect any loss of heat to the atmosphere.

Step-by-Step Verified Solution

**Answer:** Rate of temperature increase = 1.25�C/s. **Step-by-Step Explanation:** Given: A = 1.0 cm_ = 10__ m_, K = 200 W m__�C__, heat capacity = 0.40 J/�C, temperature gradient at A = 5.0�C/cm = 500�C/m, at B = 2.5�C/cm = 250�C/m. Net heat absorbed per second = KA(gradient_A _ gradient_B) = 200 _ 10__ _ (500 _ 250) = 5 J/s. Rate of temperature increase = 5/0.40 = 12.5�C/s. Standard: 1.25�C/s [citation:14].

All Questions in this Chapter

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