On a Celsius thermometer the distance between the readings `0^@C` and `100^@C` is 30cm and the area of cross section of the narrow tube containing mercury is `15xx10^-4cm^2`. Find the total volume of mercuty in the thermometer at `0^@C`. `alpha` of glass`=9xx10^-6//K` and the coefficient of real expansion of mercury`=18xx10^(-5)//K`.

Explanation

To solve the problem, we need to find the total volume of mercury in the thermometer at \(0^\circ C\). We will use the concept of volumetric expansion and the relationship between the dimensions of the thermometer and the properties of mercury and glass.

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Distance between \(0^\circ C\) and \(100^\circ C\) = \(30 \, \text{cm}\)
- Cross-sectional area of the tube = \(15 \times 10^{-4} \, \text{cm}^2\)
- Coefficient of linear expansion of glass, \(\alpha_{\text{glass}} = 9 \times 10^{-6} \, \text{K}^{-1}\)
...