The concept of Adiabatic is basically the isolation of a system in a realm where energy doesn't flow either way. Adiabatic compression and expansion is a common phenomenon harnessed in equipments and machines to heat or otherwise cool. The practical application of adiabatic can vary in design and technique, hence my question. If I have a tank of nitrogen gas at 300°C and 4500 psi and I want to cool the gas to 25°C and fill the nitrogen into a large balloon to a pressure of 20 psi, how can I harness adiabatics (especially adiabatic expansion) to cool the gas to my desired temperature between the tank and balloon.
Adiabatic expansion of nitrogen at room temperature will produce Joule-Thomson cooling. If your tank were only slightly above room temperature, the resulting balloon would be quite cold. The bad news is all real gases have an inversion temperature where the J-T coefficient becomes negative and throttling the gas to a lower pressure makes the temperature go UP. Looking at the chart on Wikipedia, I have to wonder if you (or your professor) chose that temperature because it is close to the inversion temperature of nitrogen (348 °C). Adiabatically, taking 300 °C nitrogen from 310 bar (no mixed units, please) to 1 bar, you will get a little cooling, exactly how much requires an Mollier (Pressure-Enthalpy) diagram for nitrogen. Above 350 °C, you are not going to cool it by any adiabatic process.