There are two concentric spherical shells A and B of surface area `20 cm^(2)` and `80 cm^(2)` . Surfaces ofboth the shells behave like black bodies. It is given thatthethermal conductivity ofmaterial of B is very low and that of A is very high. Initially the temperature of 4 is 400 K and that of B is 300 k. Find the rate of change of temperature of A and B. Given that the heat capacities of A and B are `50J//^(@)C` and `80J//^(@)C` respectively.

Explanation

To solve the problem step by step, we will use the principles of heat transfer, specifically focusing on radiation and the concept of heat capacity.

### Step 1: Understand the Problem
We have two concentric spherical shells, A and B, with given surface areas and temperatures. Shell A has a high thermal conductivity, while shell B has a low thermal conductivity. We need to find the rate of change of temperature for both shells.

### Step 2: Identify Given Data
- Surface area of shell A, \( A_A = 20 \, \text{cm}^2 = 20 \times 10^{-4} \, \text{m}^2 \)
- Surface area of shell B, \( A_B = 80 \, \text{cm}^2 = 80 \times 10^{-4} \, \text{m}^2 \)
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