A solid cube of side a density d and specific heat s is at temperature 400 K it is placed in an ambient temperature of 200 K take `a=0.9m,d=4.8xx10^(3)kg//m^(3),s=2.0xx10^(3)J//kg//K` stefan's constant `sigma=6xx10^(-8)W//K^(4)-m^(2)` consider the cube to be a blakc body. if the time for the temperature of the cube to drop by 5 K is 1000 X seconds, find X in nearest integer.

Explanation

To solve the problem, we need to calculate the time it takes for the temperature of a solid cube to drop by 5 K when placed in an ambient temperature of 200 K. Here are the steps to derive the solution:

### Step 1: Calculate the mass of the cube
The mass \( m \) of the cube can be calculated using the formula:
\[ m = \text{density} \times \text{volume} \]
The volume \( V \) of the cube is given by:
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