water pipes break when temperature goes down, how to estimate the energy involved? Normally low temperature is associated with lower energy state and high temperature with higher energy state. 
There is an apparent paradox when a water pipe breaks due to low temperature: when temperature goes down below 0°C/32°F, a water pipeline can break due to ice expansion inside the pipe. 
In order to break pipe, energy is required, so this the apparent paradox: decreasing energy, associated to temperature drop, causes an event (pipe break) that requires energy. 
How to evaluate the energy that breaks water pipes when temperature goes below 0°C/32°F ?
 A: When the water cools and freezes, energy is leaving. When the pipe is stressed, energy is going in. The energy to strain the pipe comes from the cooling water. Another way to realize this is that as the water expands, it must be doing work on the pipe to move it.
A: There is abundant thermal and potential energy in the liquid water which must be displaced as the water is cooled. As temperature decreases, the molecules slow down and, in the case of freezing water, spread apart. This is the source of the energy required to break the pipe.
What is unusual about water compared with most materials is that the coefficient of thermal expansion, $\frac{1}{V}\frac{\partial V}{\partial T}$, is negative for certain temperatures (around the solid-liquid phase transition). This is not a paradox, however, because thermodynamics doesn't require this value to be positive for stability.
A: Key to understanding the ability of freezing of water to break a pipe is the phase transition from liquid water to ice. Let me first discuss water freezing generally, and then I will go to the specific case of water bursting a pipe.
In ice crystal the water molecules are in a stabilized position. The stabilization comes from the formation of a particular type of bond that is called 'hydrogen bridge'. A hydrogen bridge is a much weaker form of binding than a molecular bond, but as we know: in the case of water there is a siginificant effect. 
As with any form of binding: when molecules fall into a bond there is some release of energy. Conversely, once a bond is formed input of energy is required to break that bond.
At room temperature only a small percentage of the water molecules has a hydrogen bridge going on. At room temperature the thermal motion of the water molecules is vigorous enough to break any hydrogen bridge that forms. Hydrogen bridges do form, but they don't last.
The freezing point of water is the critical point. Below the freezing point the rate of formation of hydrogen bridges exceeds the rate of dissolution of hydrogen bridges.
When you have an amount of water, and you continuously withdraw heat then at the freezing point the graph of temperature versus time will flatline for a while. It's only when all of the water is frozen solid that the temperature starts dropping again.
Imagine ice crystal, in contact with liquid water. The water molecules do not all move at the same speed. Given how they are bumping into each other all the time there is a statistical distribution of speeds. All the time it is the slowest water molecules that get "stuck" to the ice crystal, forming hydrogen bridges. That is, of the available water molecules the lowest energy ones transition to the ice form. So the remaining water molecules are slightly more energetic than the average. In effect the process of freezing replenishes heat that is being withdrawn.
Now to the case of water in a pipe.
When the temperature is several degrees below freezing then the pressure increases because it is energetically favorable to transition to the ice crystal form. 
A sufficiently strong pipe would prevent the water inside from freezing completely. Since ice has a larger volume than water: the higher the pressure, the higher the energetic cost of going from the liquid form to the ice form. 
However, in the case of the pipes we're talking about here the amount of pressure that the freezing water can exert is more than the pipe can withstand, and the pipe bursts.
