What causes the adiabatic lapse rate?

The adiabatic lapse rate is commonly explained as being proportional to the work done on a fluid parcel as its volume changes in response to an increase in pressure. According to this explanation the adiabatic lapse rate would increase with both pressure and the fluidʹs compressibility, but this is not the case. Rather, the adiabatic lapse rate is proportional to the thermal expansion coefficient and is independent of the fluidʹs compressibility. Here we show that the adiabatic lapse rate is independent of the increase in the internal energy that a parcel experiences when it is compressed. We explain what is missing from the traditional explanation of the adiabatic lapse rate and we explore the thermodynamic cause of the adiabatic lapse rate. In particular, we seek to explain how the adiabatic lapse rate can be negative in cool fresh water.