Volume of the bulb of a mercury thermometer at `0^(@)C` is `V_(@)` and area of cross section of the capillary tube is `A_(0)`, coefficient of linear expansion of glass is `alpha_(g)`, and the cubical expansion of mercury is `gamma_(m)`. If the mercury fills the bulb at `0^(@)C`, find the length of mercury column in thermometer at `T^(@)C`

Explanation

To find the length of the mercury column in the thermometer at temperature \( T \) °C, we can follow these steps:

### Step 1: Understand the thermal expansion of mercury and glass
When the temperature of the mercury rises, both the mercury and the glass of the thermometer will expand. The volume expansion of mercury is given by the formula:
\[ \Delta V_m = V_0 \cdot \gamma_m \cdot T \]
where \( V_0 \) is the initial volume of the mercury at \( 0 \) °C, \( \gamma_m \) is the coefficient of cubical expansion of mercury, and \( T \) is the change in temperature.
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