(a) Draw a labelled diagram of a vacuum flask. Explain how its construction minimizes heat exchange with the surroundings. (b) State Boyle's law. A thread o...

(a) Labelled diagram of a vacuum flask

A vacuum flask minimizes heat exchange as follows:

• The vacuum between the double glass walls prevents heat transfer by conduction and convection.
• The silvered surfaces reflect thermal radiation, thereby reducing heat transfer by radiation.
• The cork or plastic stopper is a poor conductor of heat, while the narrow neck reduces convection and evaporation through the top.

(b) Boyle's law

Boyle's law states that the volume of a fixed mass of gas is inversely proportional to its pressure, provided that its temperature remains constant.

Thus,

\[PV=\text{constant}\qquad\text{or}\qquad P_1V_1=P_2V_2.\]

Since the capillary tube has a uniform cross-sectional area, the volume of the trapped air is proportional to its length. Therefore,

\[P_1L_1=P_2L_2.\]

Initially, with the open end uppermost, the pressure of the trapped air is:

\[P_1=76+15=91\ \text{cm Hg},\qquad L_1=20\ \text{cm}.\]

(i) Tube held horizontally

There is no vertical mercury head acting on the trapped air, so:

\[P_2=76\ \text{cm Hg}.\]

\[91\times20=76\times L_2\]

\[L_2=\frac{1820}{76}=23.95\ \text{cm}\approx24\ \text{cm}.\]

Length of air column = \(24\ \text{cm}\).

(ii) Tube held vertically with the open end underneath

The mercury thread now reduces the pressure on the trapped air:

\[P_2=76-15=61\ \text{cm Hg}.\]

\[91\times20=61\times L_2\]

\[L_2=\frac{1820}{61}=29.84\ \text{cm}\approx30\ \text{cm}.\]

Length of air column = \(30\ \text{cm}\).

(c) A clinical thermometer has a limited range, usually about \(35^\circ\text{C}\) to \(42^\circ\text{C}\). In boiling water at \(100^\circ\text{C}\), the mercury expands excessively and may force its way into the upper end of the capillary tube, cracking or damaging the thermometer. It should therefore not be sterilized in boiling water.