I have a problem when calculating the temperature drop after a pressure release in a water sample. I use the following expression for the adiabatic temperature change: (delta T/delta P)= alpha*T*V/Cp where alpha is the thermal expansion coefficient, T is the temperature in Kelvin, V is the specific volume and Cp is the specific heat. I have appropriate equations to calculate all these parameters (all dependent on both pressure and temperature). I calculate the temperature drop numerically integrating this equation with 0.1 MPa pressure increments. Nevertheless, for expansions from 100 MPa and -10ºC, I obtain surprising results: a little temperature increase (sample temperature after expansion is about -9.8ºC). That is due to the negative sign of the thermal expansion coefficient at low pressures and temperatures. However, in practice, I record a temperature drop in the sample (about -10.3ºC). Is the equation employed valid for negative thermal expansion coefficients??? How can I explain this behaviour??? Thanks in advance.