Question

At the bottom of an old mercury-in-glass thermometer is a 54 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 2.0×10⁻² 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.

Answer 1

To determine the expansion of the mercury into the capillary, we can use the equation for the volume of a cylindrical tube and solve for the height. Plugging in the given values, the mercury would expand approximately 136 mm into the capillary when the temperature changes by 1.0 °C.

Step-by-step explanation:

To determine the expansion of the mercury into the capillary, we can use the equation for the volume of a cylindrical tube:

V = πr^2h

where V is the volume, r is the radius, and h is the height. We can rearrange the equation to solve for h:

h = V/(πr^2)

Plugging in the given values, we have:

h = 54 mm³ / (π(2.0×10⁻² mm)²)

Calculating this gives us:

h ≈ 136 mm

Therefore, the mercury would expand approximately 136 mm into the capillary when the temperature changes by 1.0 °C.