Coefficient of linear expansion of ice As ice is heated it starts to melt and as far as I know water expands on cooling and contract on melting or heating but I do not understand why is coefficient of linear expansion of ice is calculated to be approximately equal to 50×10^-6 K¹-. What does this mean?
 A: The coefficient of linear expansiveness of ice is a measure of the fractional change in the length of a specimen of ice for a 1 degree change in temperature.
It is a property of water in the solid phase of water.
So around but below $0^\circ \rm C$ the fractional change in the length of a specimen of ice is $50 \times 10^{-6}$ for ever degree change in the temperature as long as the temperature is such that you have only ice present.
The value of this coefficient decreases as the temperature decreases and actually becomes negative below approximately $-250^\circ \rm C$ as shown in the graph below.
 
A: Ice does contract in volume when it melts and the water thus formed keeps contracting until $4^{\circ}C $. After that temperature, if you heat it further it starts expanding again. In fact, a litre used to be defined as the volume of water that weighs $1kg$ at $4^{\circ}C$.
The point is: changes in volume do not happen only during phase changes. If you heat a metal it will expand and you don't need to melt it for that volume change to happen. Once you get that the definition of the coefficient of linear expansion is easy to follow.
It is the length expansion per unit length suffered by a body when its temperature is raised by $1K$. So if you have a rod of length $1m$ then the amount by which it expands when you heat it by $1K$ is its coefficient of linear expansion. 
