Lowering of temperature in expansion valve of refrigerator We know that the high pressure liquid refrigerant (comming from condenser) passes through the expansion valve and lowers the temperature (due to decrease in pressure).
My Question:
From the formula pV = nRT:
(p1V1) / T1 = (p2V2) / T2    [ n & R are constant]
So, if the pressure (p2) decreases, either volume (V2) should increase or temperature (T2) decrease.
Then, why only the temperature (T2) decreases. It can rather be isothermal process in which temperature remains constant (T1) and volume (V2) may increase.
Moreover, this process of expansion of gas is very fast and we know that transfer of heat will not get sufficient time. So temperature should remain conatant and volume should increase.
But actually, it does not happen. Why?
 A: Refrigerant is NOT an ideal gas, so the ideal gas law is inappropriate in this application.  The temperature of the refrigerant is related to the pressure that the refrigerant is experiencing through the Antoine equation.  See https://en.wikipedia.org/wiki/Antoine_equation.  As the refrigerant flows through the expansion valve, it experiences a significant drop in pressure.  Due to this, the refrigerant is superheated on the low pressure side of the expansion valve, and it boils as a result.  The heat required for boiling comes from the refrigerant itself, so the temperature of the refrigerant rapidly drops as boiling occurs, and this temperature drop does NOT require any heat transfer to or from the environment.  Thus, on the low pressure side of the expansion valve, there is a mixture of low pressure vapor and low pressure liquid that goes to the evaporator.
A: As you noted, the refrigerant is a liquid as it passes through the expansion valve, and it is not appropriate to apply gas laws to a liquid.  To understand what happens in the expansion valve you have to start at the compressor.  After the compressor exhausts high temperature and high pressure gas to the condenser its piston moves down and creates a region of low pressure. Low temperature gas flows from the evaporator to the lower pressure compressor and pressure in the evaporator drops. The expansion valve senses the drop in pressure and allows hot high pressure refrigerant to flow into the evaporator through the valve until the pressure in the evaporator recovers. When the refrigerant encounters the low pressure two things happen.  First, some of the refrigerant evaporates. The refrigerant is a super heated fluid at the ambient pressure of the evaporator so its vapor pressure is higher than the ambient pressure causing it to boil. Boiling removes the highest energy particles from the liquid lowering the average kinetic energy of the remaining particles and thus the temperature.This is called evaporative cooling. The process will continue until the liquid has cooled to the point where its vapor pressure is the same as the ambient pressure. The gas that is produced cooling the warm liquid will have a higher pressure than the ambient pressure in the evaporator, so it will expand. As the gas expands, it will compress the ambient gas thus doing work to it and transferring energy to it. This loss of energy cools the gas as it expands.
