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Mechanical Properties Of Fluids

Question
CBSEENPH11019320

What is temperature coefficient of cubical expansion? Find the volume of a cube when it is heated through θ°C.

Solution

The ratio of the increase in volume per unit original volume per unit rise in temperature is defined as the temperature coefficient of cubical expansion.
It is represented by γ. 
Consider a cube of volume V0 at 0°C.
If the temperature of cube  is increased by θ°C, it will expand.
The increase in the volume of cube is, 
(i) proportional to the original volume 
(ii) proportional to rise in temperature, 
i.e.           increment straight V proportional to straight V subscript 0 straight theta 
 
               increment straight V equals γV subscript 0 straight theta 
The volume of cube at temperature straight theta degree straight C is, 
                straight V equals straight V subscript 0 plus γV subscript 0 straight theta space equals space SV subscript 0 left parenthesis 1 plus γθ right parenthesis