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QPages 98-102: Q45: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q45 Solution: A cubical block of mass 1.0 kg and edge 5.0 cm is heated to…

A cubical block of mass 1.0 kg and edge 5.0 cm is heated to 227�C. It is kept in an evacuated chamber maintained at 27�C. Assuming that the block emits radiation like a blackbody, find the rate at which the temperature of the block will decrease. Specific heat capacity of the material of the block is 400 J kg−1 K−1400 \text{ J kg}^{-1} \text{ K}^{-1}.

Step-by-Step Verified Solution

**Answer:** Rate of temperature decrease = 0.056�C/s. **Step-BY-Step Explanation:** Given: m = 1.0 kg, edge = 5.0 cm = 0.05 m, T = 227�C = 500 K, T_ = 27�C = 300 K, c = 400 J/kg-K, _ = 6.0 _ 10__. A = 6 _ (0.05)_ = 0.015 m_.
P=σA(T4−T04)=6.0×10−8×0.015×(5004−3004)=22.4 WP = \sigma A(T^4 - T_0^4) = 6.0 \times 10^{-8} \times 0.015 \times (500^4 - 300^4) = 22.4 \text{ W}
Rate = P/(mc) = 22.4/(1 _ 400) = 0.056�C/s.

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