Final answer:
To determine the height of the mercury column at 40°C, a proportion between the temperature difference and corresponding height change is set up. Solving this proportion indicates that the mercury column would be 12 cm high at 40°C.
Step-by-step explanation:
The student is asking how to determine the height of the mercury column in a thermometer at 40°C given that the height is 3 cm at the melting point of ice (0°C) and 18 cm at the steam point (100°C). Assuming a linear relationship between temperature and the mercury column height, we can use the concept of temperature scales and proportions to solve this problem.
To find the height at 40°C, we establish a proportion where the total temperature range (100°C) corresponds to the total length change (18cm - 3cm), and the desired temperature (40°C) will correspond to the unknown height (h) change from 0°C.
The proportion is therefore (h - 3 cm) / (18 cm - 3 cm) = 40°C / 100°C, which simplifies to h - 3 cm = 15 cm × 0.4. Solving for h gives us h = 9 cm + 3 cm, which equals 12 cm. Hence, at 40°C the height of the mercury column would be 12 cm.