(a) What is meant by the statement: The linear expansivity of a solid is \(1.0 \times 10^{-5}K^{-1}\)? (b)(i) Describe an experiment to determine the linear...

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(a) Meaning of a linear expansivity of \( 1.0 \times 10^{-5}\,\text{K}^{-1} \)

It means that each unit length of the solid increases by \( 1.0 \times 10^{-5} \) of its original length for every 1 K (1 °C) rise in temperature. For example, a 1 m length would lengthen by \( 1.0 \times 10^{-5}\,\text{m} \) for each degree rise.

(b)(i) Experiment to determine the linear expansivity of a steel rod

Measure the original length \( l_0 \) of the steel rod and its initial temperature \( \theta_1 \). Place the rod in a jacket through which steam is passed, with one end fixed and the other end pressing against a micrometer/spherometer (or an optical lever). Record the increase in length \( \Delta l \) as the rod is heated to the steam temperature \( \theta_2 \). The linear expansivity is

\[ \alpha = \frac{\Delta l}{l_0(\theta_2 - \theta_1)} \]

(b)(ii) Safety gap between rails

Expansion of one bar: \( \Delta l = l_0 \, \alpha \, \Delta\theta \)

\[ \Delta l = 3 \times (1.0 \times 10^{-5}) \times (41 - 29) \]

\[ \Delta l = 3 \times 1.0 \times 10^{-5} \times 12 = 3.6 \times 10^{-4}\,\text{m} = 0.36\,\text{mm} \]

A gap of about 0.36 mm must be left between successive bars.

(c) Advantages and disadvantages of thermal expansion of solids

Three advantages:

• Fitting a metal tyre or ring onto a wheel (heat to expand, then cools and grips tightly).
• Hot riveting of metal plates (rivet contracts on cooling and clamps the plates firmly).
• Use in bimetallic strips for thermostats, thermometers and fire alarms.

Two disadvantages:

• Railway lines and bridges may buckle or bend if no expansion gaps are provided.
• Overhead telephone/electric cables sag in hot weather and may snap when they contract in cold weather; tight-fitting parts may jam or crack.