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 use the thermal expansion formula. The formula states that the change in length is equal to the initial length multiplied by the coefficient of linear expansion and the change in temperature.

Given data:
Reservoir volume (V) = 43 mm^3
Capillary radius (r) = 1.9 × 10^(-2) mm
Change in temperature (ΔT) = 1.0 °C

First, let's calculate the initial length of the mercury column in the capillary. The length can be found using the formula for the volume of a cylinder:

Volume of the reservoir (V) = πr^2h

Since we know the radius (r) and volume (V) of the reservoir, we can rearrange the formula to solve for the initial height (h) of the mercury column:

h = V / (πr^2)

Substituting the values, we get:

h = 43 mm^3 / (π * (1.9 × 10^(-2) mm)^2)

Now, we can calculate the change in length (ΔL) using the formula for thermal expansion:

ΔL = L * α * ΔT

Where L is the initial length, α is the coefficient of linear expansion, and ΔT is the change in temperature.

To calculate ΔL, we need the coefficient of linear expansion for mercury. For mercury, α is approximately 1.81 × 10^(-4) 1/°C.

Using the calculated value of h and the coefficient of linear expansion, we can now calculate ΔL:

ΔL = h * α * ΔT

Substituting the values, we get:

ΔL = (43 mm^3 / (π * (1.9 × 10^(-2) mm)^2)) * (1.81 × 10^(-4) 1/°C) * (1.0 °C)

Now let's simplify and calculate the value:

ΔL ≈ 1.51 mm

Therefore, the mercury would expand approximately 1.51 mm into the capillary when the temperature changes by 1.0 °C.