Answer:
The liquid column in a liquid-in-glass thermometer is designed to expand or contract with temperature changes. The length of the column is proportional to the temperature of the liquid.
Given that the liquid column is 2.0 cm long at 0°C and expands by 10.0 cm when heated to 100°C, we can calculate the length of the column at any temperature between 0°C and 100°C using the following formula:
L = L0 + kΔT
where L is the length of the column at the desired temperature, L0 is the length of the column at 0°C, k is the constant of proportionality, and ΔT is the change in temperature.
Using the given values, we can find the constant of proportionality:
k = ΔL/ΔT = (10.0 cm - 2.0 cm)/(100°C - 0°C) = 0.08 cm/°C
Now, we can use the formula to find the length of the column at any temperature between 0°C and 100°C. For example, at 50°C:
L = 2.0 cm + (0.08 cm/°C)(50°C - 0°C) = 6.0 cm
Therefore, the length of the liquid column in the liquid-in-glass thermometer would be 6.0 cm at 50°C.