(a) The tube of a mercury thermometer has an inside diameter of 0.140 mm . The bulb has volume o

step 1 So we have a mercury bulb, let's say the volume of the mercury bulb was V, which we know is 0 .2

(a) The tube of a mercury thermometer has an inside diameter...

(a) The tube of a mercury thermometer has an inside diameter of 0.140 $\mathrm{mm}$ . The bulb has volume of 0.275 $\mathrm{cm}^{3} .$ How far will the thread of mercury move when the temperature changes from $10.5^{\circ} \mathrm{C}$ to $33.0^{\circ} \mathrm{C}$ ? Take into account expansion of the Pyrex glass. (b) Determine a formula for the change in length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

Key Concepts

Thermal Expansion

Thermal expansion refers to the tendency of matter to change its shape, area, volume, and density in response to a change in temperature. For fluids like mercury, this typically results in an increase in volume as the temperature rises, a phenomenon that is quantitatively described by the material's thermal expansion coefficient.

Volume Expansion Coefficient

The volume expansion coefficient (often denoted as ?) characterizes how the volume of a material changes with temperature. It is defined as the fractional change in volume per unit temperature increase and is central in calculating the volume change of mercury in a thermometer when the temperature varies.

Linear Expansion Coefficient

The linear expansion coefficient (commonly denoted as ?) describes the fractional change in a material’s length per unit temperature change. In the context of thermometers, this coefficient is important for accounting for the expansion of the Pyrex glass which comprises the bulb and the tube that contains the mercury.

Relationship Between Volume and Linear Changes

In systems where a fluid is confined within a tube, the change in the length of the fluid column is related to the change in volume of the fluid as well as the cross-sectional area of the tube. This relationship is key to determining the displacement of the mercury as its volume increases with temperature.

Derivation of a Displacement Formula

Deriving a displacement formula for the mercury column involves linking the volumetric expansion of the mercury to its corresponding linear displacement in the tube. This derivation accounts for the change in volume in the bulb and divides it by the cross-sectional area of the tube, while also incorporating any compensating effects due to the thermal expansion of the container material.

Transcript

Please give Ace some feedback