If the volume of block of metal changes by x % when it is heated through θ°C, then what is the coefficient of linear expansion of the metal?

Solution

Let V be the volume of the block and

straight alpha

the temperature coefficient of linear expansion of the block.
Therefore coefficient of cubical expansion of block is 3

straight alpha

.
If the temperature of block is increased by

straight theta

, then change in volume of block is given by,

increment straight V space equals space 3 αVθ

The percentage change in volume of block is,

fraction numerator increment straight V over denominator straight V end fraction 100 equals 300 αθ

But percentage change in volume is x %.
Therefore,

300 αθ equals straight x

rightwards double arrow

straight alpha equals open parentheses fraction numerator straight x over denominator 300 space straight theta end fraction close parentheses straight C presuperscript straight o superscript negative 1 end superscript

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