First slide

Thermal expansion

Question

The variation of length of a substance along three principal directions with temperature is shown in the figure. The average superficial expansivity of the substance is

Moderate

A

26.67×10^–5/°C
B

13.67×10^–5/°C
C

16.67×10^–5/°C
D

14.67x10^-5/ $°$ C

Solution

${\alpha _x} = \frac{{2004.0 - 2000.0}}{{2000.0 \times (10 - 0)}} = 2 \times {10^{ - 4}}/^\circ C$
${\alpha _y} = \frac{{2003.2 - 2000.0}}{{2000.0 \times (10 - 0)}} = 1.6 \times {10^{ - 4}}/^\circ C$
${\alpha _z} = \frac{{2000.8 - 2000.0}}{{2000.0 \times 10}} = 0.4 \times {10^{ - 4}}/^\circ C$
$\alpha = \frac{{{\alpha _x} + {\alpha _y} + {\alpha _z}}}{3} = \frac{{(2 + 1.6 + 0.4) \times {{10}^{ - 4}}}}{3}$
$= \frac{4}{3} \times {10^{ - 4}}/^\circ C$
$\beta = 2\alpha = 26.67 \times {10^{ - 5}}/^\circ C$

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