A solid copper sphere of density `rho`, specific heat c and radius r is at temperature `T_1`. It is suspended inside a chamber whose walls are at temperature `0K`. What is the time required for the temperature of sphere to drop to `T_2`? Take the emmissivity of the sphere to be equal to e.

Explanation

To solve the problem of determining the time required for the temperature of a solid copper sphere to drop from \( T_1 \) to \( T_2 \) in a chamber at \( 0K \), we will follow these steps:

### Step 1: Understand the Heat Loss Mechanism
The sphere loses heat through radiation. The rate of heat loss \( \frac{dQ}{dt} \) can be expressed using the Stefan-Boltzmann law:
\[ \frac{dQ}{dt} = e \sigma A (T^4 - T_0^4) \]
where:
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