Question
Derive the relation between 
and β. Assume that coefficient of linear expansions are same in all directions.
Solution
Consider a rectangular sheet of sides L0 and B0 at 0°C.
Therefore the area of sheet at 0°C is S0 = L0B0.
When the sheet is heated, area of the plate will increase due to increase in the length and breadth.
If
is coefficient of linear expansion and β is coefficient of superficial expansion, then at temperature θ°C,
and
But
∴![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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Since,
therefore using binomial expansion,
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Therefore the area of sheet at 0°C is S0 = L0B0.
When the sheet is heated, area of the plate will increase due to increase in the length and breadth.
If
is coefficient of linear expansion and β is coefficient of superficial expansion, then at temperature θ°C, and
But
∴
Since,
therefore using binomial expansion,
