A chilled water system is filled with water at a temperature between 50 and 60ºF. When the chiller is turned on, the temperature of the water drops to 45ºF. When the water contracts, the system pressure drops, and the fill valve allows more water to enter the system to maintain the system pressure.
If the chiller shuts down and the water in the system warms up to room temperature, the rise in temperature from 45º to ambient will cause the water in the system to expand. Without an expansion tank, the relief-valve would blow. The tank can be smaller than the one used in a hot water system, because the temperature is rising from 45ºF to ambient, instead of from ambient to 200ºF.