Final answer:
The volume of the bulb needed for a mercury thermometer with the given specifications is approximately 2.747 cm³. This is calculated by dividing the volume change required in the capillary tube for a 40°C temperature change by the product of the mercury's volumetric expansion coefficient and the temperature range.
Step-by-step explanation:
The student is asking how to calculate the volume of the bulb required for a mercury thermometer, assuming the capillary cross-section and the volumetric expansion coefficient of mercury are known. The thermometer is designed such that there's a 20 cm distance between the -5°C and 35°C markings.
The temperature range from -5°C to 35°C is a difference of 40°C. Given that the volumetric expansion coefficient (β) is 0.182 C-1 and the cross-sectional area of the capillary tube (σ) is 0.1 mm2, we can calculate the volume change that occurs over these 40 degrees. The volume change (ΔV) in the capillary corresponds to the length change (ΔL) times the cross-sectional area (σ).
Using the equation ΔV = ΔL * σ, we can find that the volume change is 20 cm * 0.1 mm2. We need to convert 20 cm to mm to ensure consistent units, which gives us 200 mm. Hence, ΔV = 200 mm * 0.1 mm2 = 20 mm3.
Now, we need to calculate the volume expansion that would occur in the bulb given the coefficient of volumetric expansion. Using the formula ΔV = V0 * β * ΔT, where ΔT is the temperature change (40°C), we can find the initial volume (V0) that would expand to the 20 mm3 in the tube. Rearranging and solving for V0 gives us V0 = ΔV / (β * ΔT).
Therefore, the required volume of the bulb would be 20 mm3 / (0.182 C-1 * 40°C), which simplifies to 20 mm3 / 7.28 = approximately 2.747 mm3 or 2.747 cm3.