Two identical solid copper spheres P and Q

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

Two identical solid copper spheres P and Q, each of radius

5\,\text{cm}

, are initially at

300\,\text{K}

. Sphere P is coated with lamp black having average absorptive power

0.95

, whereas sphere Q is nickel-polished with average absorptive power

0.10

. The spheres are suddenly introduced into a large evacuated furnace maintained uniformly at

800\,\text{K}

. Heat exchange can take place only by radiation. Let each sphere have mass

m

and specific heat capacity

c

. (i) Write an expression for the net power absorbed by each sphere immediately after being placed in the furnace. (ii) Using the result of part (i), derive the ratio of the initial rates of rise of temperature

\left(\dfrac{dT}{dt}\right)

for spheres P and Q, assuming their own temperatures are still close to

300\,\text{K}

. (iii) On the basis of your derivation, indicate which sphere will reach the furnace temperature sooner and estimate how many times faster its initial heating is compared with the other sphere.

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