(a) Define the apparent cubic… | Physics

Question 1 Report

(a) Define the apparent cubic expansivity of a liquid

(b)(i) Describe with the aid of a labelled diagram, an experiment to determine the apparent cubic expansivity of a liquid.

(ii) State two precuations that should be taken to ensure accurate results.

(c) A density glass bottle contains 44.25g of a liquid at 0°C and 42.02g at 50°C. Calculate the real cubic expansivity of the liquid. (Linear expansivity of glass = 1.0 x 10-5K\(^{-1}\))

Answer

(a) The apparent cubic expansivity of a liquid is the apparent increase in volume per unit original volume of the liquid per unit rise in temperature. It is the expansion observed when the expansion of the containing vessel is not allowed for.

(b)(i) Determination of apparent cubic expansivity

The apparatus is arranged as shown below.

Labelled arrangement for determining the apparent cubic expansivity of a liquid.

A clean, dry density bottle fitted with a stopper having a fine capillary hole is weighed empty. Let its mass be \(M_1\). It is filled completely with the liquid at the initial temperature \(T_1\), the stopper is inserted, and the outside is wiped dry. The mass of the bottle and liquid is found as \(M_2\).

The bottle is suspended in a water bath, with the stopper and capillary orifice above the water level. A thermometer is placed in the bath. The water is heated slowly to a final temperature \(T_2\). As the liquid expands, some of it escapes through the capillary hole. Heating is continued until no further liquid escapes at \(T_2\).

The bottle is removed, allowed to cool, wiped dry and weighed again. Let its final mass be \(M_3\).

Thus,

\[\text{mass of liquid expelled}=M_2-M_3\]

\[\text{mass of liquid remaining}=M_3-M_1\]

\[\Delta T=T_2-T_1\]

Therefore, the apparent cubic expansivity is

\[\gamma_a=\frac{M_2-M_3}{(M_3-M_1)(T_2-T_1)}.\]

(ii) Precautions

Heat the water bath slowly and stir it so that the liquid and the bath are at a uniform temperature.
Read the thermometer at eye level to avoid parallax error.
Keep the capillary orifice above the water level and wipe the bottle completely dry before each weighing.

(c) Calculation of the real cubic expansivity

For a temperature rise of \(50\,\mathrm{K}\):

\[\gamma_a=\frac{44.25-42.02}{42.02\times 50}\]

\[\gamma_a=\frac{2.23}{2101}=1.06\times10^{-3}\,\mathrm{K^{-1}}.\]

The cubic expansivity of the glass bottle is

\[\gamma_g=3\alpha_g=3(1.0\times10^{-5})=3.0\times10^{-5}\,\mathrm{K^{-1}}.\]

Since \(\gamma_r=\gamma_a+\gamma_g\),

\[\gamma_r=1.06\times10^{-3}+3.0\times10^{-5}\]

\[\boxed{\gamma_r=1.09\times10^{-3}\,\mathrm{K^{-1}}}.\]

Read lesson note on Temperature And Its Measurement (JAMB)

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