The volume occupied by a thin- wall brass vessel and the volume of a solid brass sphere are the same and equal to `1,000 cm^(3) at 0^(@)C`. How much will the volume of the vessel and that of the sphere change upon heating to `20^(@)C`? The coefficieny of linear expansion of brass is `alpha = 1.9 xx 10^(-5)`.

Explanation

To solve the problem of how much the volume of a thin-wall brass vessel and a solid brass sphere change upon heating from 0°C to 20°C, we will follow these steps:

### Step 1: Identify the initial conditions
- The initial volume \( V_0 \) of both the vessel and the sphere is given as \( 1000 \, \text{cm}^3 \) at \( 0°C \).
- The initial temperature \( T_0 \) is \( 0°C \) and the final temperature \( T_f \) is \( 20°C \).

### Step 2: Calculate the change in temperature
- The change in temperature \( \Delta T \) can be calculated as:
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