What is temperature coefficient of superficial expansion? Find the area of a sheet when it is heated through θ°C.

Solution

The temperature coefficient of superficial expansion is defined as the ratio of the increase in area per unit original area per unit rise in temperature.
It is represented by β.
Consider a sheet of area S₀ at 0°C.
If we increase the temperature of sheet by 0°C, it will expand.
The increase in the area of sheet is,
(i) proportional to the original area
(ii) proportional to rise in temperature,
i.e. $increment straight S proportional to straight S subscript 0 straight theta$
$rightwards double arrow$ $increment straight S space equals space βS subscript 0 straight theta$
The area of sheet at temperature $straight theta degree straight C$ is
$straight S equals straight S subscript 0 plus βS subscript 0 straight theta space equals straight S subscript 0 left parenthesis 1 plus βθ right parenthesis$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

What is temperature coefficient of superficial expansion? Find the area of a sheet when it is heated through θ°C.

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