At the bottom of an old mercury-in-glass thermometer is a 43-mm3 reservoir filled with mercury. When the thermometer was placed under your tongue, the warmed mercury would expand into a very narrow cylindrical channel, called a capillary, whose radius was 1.9 × 10-2 mm. Marks were placed along the capillary that indicated the temperature. Ignore the thermal expansion of the glass and determine how far (in mm) the mercury would expand into the capillary when the temperature changed by 1.0 C°.

To determine how far the mercury would expand into the capillary when the temperature changes, we need to calculate the change in volume of the mercury.

The change in volume can be calculated using the formula:
ΔV = V₀ * β * ΔT

Where:
ΔV is the change in volume
V₀ is the initial volume of the mercury in the reservoir
β is the volumetric coefficient of thermal expansion of mercury
ΔT is the change in temperature

In this case, V₀ is given as 43 mm³.

The volumetric coefficient of thermal expansion of mercury, β, can be found in the literature. It is the change in volume per unit volume per degree Celsius (mm³/°C).

Once we have the change in volume, we can find the change in length by using the formula:
ΔL = (ΔV / A)

Where:
ΔL is the change in length
A is the cross-sectional area of the capillary

The cross-sectional area of the capillary can be calculated using the formula:
A = π * r²

Where:
A is the cross-sectional area
r is the radius of the capillary

Now let's substitute the given values into the formulas:

V₀ = 43 mm³
β (volumetric coefficient of expansion of mercury) = ? (we need to find this value)
ΔT = 1.0 °C
r (radius of the capillary) = 1.9 × 10⁻² mm

First, we need to find the value of β. According to the literature, the volumetric coefficient of thermal expansion of mercury is approximately 181 × 10⁻⁶ °C⁻¹.

Now we can calculate the change in volume:

ΔV = V₀ * β * ΔT
ΔV = 43 mm³ * 181 × 10⁻⁶ °C⁻¹ * 1.0 °C

Next, we can calculate the change in length:

A = π * r²
ΔL = ΔV / A

Finally, we can substitute the values into the equations and find the change in length of the mercury in the capillary.

To determine how far the mercury would expand into the capillary when the temperature changes by 1.0 °C, we can use the formula for the expansion of a cylindrical object:

ΔV = α * V * ΔT

Where:
ΔV = change in volume
α = coefficient of volume expansion
V = initial volume
ΔT = change in temperature

In this case, we can assume that the volume of mercury in the reservoir remains constant, and the change in volume occurs only in the capillary. Therefore, we can rewrite the formula as:

ΔV = α * V_capillary * ΔT

Let's calculate the change in volume of the mercury in the capillary reservoir:

V_capillary = π * r^2 * h_capillary

Where:
π ≈ 3.14159 (pi)
r = radius of the capillary
h_capillary = height of the capillary

Given that the radius of the capillary (r) is 1.9 × 10^(-2) mm = 1.9 × 10^(-5) cm, and we need to convert it to cm:

r = 1.9 × 10^(-5) cm

We also need to determine the height of the capillary (h_capillary). Unfortunately, the height is not given in the question. If you provide the height of the capillary, I can continue the calculation.