Expanding gas through a turbine results in a colder temperature compared to expansion through a valve due to the distribution of potential energy. In valve expansion, most potential energy converts to kinetic energy of the gas molecules, increasing their random motion and temperature. Conversely, turbine expansion converts some potential energy into mechanical work, reducing the random kinetic energy of the gas molecules. This leads to a lower temperature in the gas after expansion. The discussion references the First Law of Thermodynamics, explaining the relationship between heat energy, internal energy, and work done during the expansion process.
