We would like to make a vessel whose volume does not change with temperature . We can use brass and iron `(beta_(brass) = 6 xx10^(-5) // K and beta_(iron) = 3.55 xx 10^(-5)//K)` at create a volume of 100 c c. How do you think you can achieve this.

Explanation

To create a vessel whose volume does not change with temperature using brass and iron, we need to consider the thermal expansion properties of both materials. The goal is to find the appropriate volumes of brass and iron at 0 degrees Celsius such that their combined volume remains constant when the temperature changes.

### Step-by-Step Solution:

1. **Understand the Coefficients of Volume Expansion**:
- The coefficient of volume expansion for brass is given as \( \beta_{brass} = 6 \times 10^{-5} \, \text{K}^{-1} \).
- The coefficient of volume expansion for iron is given as \( \beta_{iron} = 3.55 \times 10^{-5} \, \text{K}^{-1} \).

...