ABSTRACT
The amount by when the coefficient of linear expansion of the material and is represented by α (Greek alpha). The units of the coefficient of linear expansion are m/(mK), although it is usually quoted as just /K or K−1. For example, copper has a coefficient of linear expansion value of 17 × 10−6 K−1, which means that a 1 m long bar of copper expands by 0.000017 m if its temperature is increased by 1 K (or 1◦C). If a 6 m long bar of copper is subjected to a temperature rise of 25 K then the bar will expand by (6 × 0.000017 × 25) m, i.e. 0.00255 m or 2.55 mm. (Since the Kelvin scale uses the same temperature interval as the Celsius scale, a change of temperature of, say, 50◦C, is the same as a change of temperature of 50 K.) If a material, initially of length L1 and at a temperature of t1 and having a coefficient of linear expansion α, has its temperature increased to t2, then the new length L2 of the material is given by:
New length = original length + expansion i.e. L2 = L1 + L1α(t2 − t1) i.e. L2 = L1[1 + α(t2 − t1)] (1) Some typical values for the coefficient of linear expansion include:
Aluminium 23 × 10−6 K−1 Brass 18 × 10−6 K−1 Concrete 12 × 10−6 K−1 Copper 17 × 10−6 K−1 Gold 14 × 10−6 K−1 Invar (nickel-steel alloy) 0.9 × 10−6 K−1 Iron 11-12 × 10−6 K−1 Nylon 100 × 10−6 K−1 Steel 15-16 × 10−6 K−1 Tungsten 4.5 × 10−6 K−1 Zinc 31 × 10−6 K−1
Problem 1. The length of an iron steam pipe is 20.0 m at a temperature of 18◦C. Determine the length of the pipe under working conditions when the temperature is 300◦C. Assume the coefficient of linear expansion of iron is 12 × 10−6 K−1
1 1 ◦C, t2 = 300◦C and α = 12 × 10−6 K−1. Length of pipe at 300◦C is given by:
L2 = L1[1 + α(t2 − t1)] = 20.0[1 + (12 × 10−6)(300 − 18)] = 20.0[1 + 0.003384] = 20.0[1.003384]
= 20.06768 m i.e. an increase in length of 0.06768 m or 67.68 mm.
