Physics: Principles with Applications (7th Edition)

As the gas expands, its volume increases and it does positive work W on its surroundings. Since Q = 0 for an adiabatic process, the first law of thermodynamics $\Delta U = Q-W$ shows that the internal energy must decrease. For an ideal gas, the temperature is proportional to the gas’s internal energy so the temperature decreases. Use the ideal gas law, PV = nRT. If the volume increases as the temperature decreases, the pressure must decrease.