2 moles of an ideal gas expands isothermally and adiabatically from a volume of 2 L to 20 L inside a

Question

2 moles of an ideal gas expands isothermally and adiabatically from a volume of 2 L to 20 L inside a rigid, perfectly insulated, and evacuated container. Which of the following accurately describes the thermodynamic parameters for this process?

Professor PC Thomas Classes · Answer

(a) : The process describes free expansion of an ideal gas into a vacuum. Because it expands against zero external pressure ($P_{ext} = 0$), the work done is strictly zero ($W = 0$). Since the container is perfectly insulated, no heat is exchanged ($q = 0$). According to the first law of thermodynamics ($\Delta U = q + W$), the change in internal energy is also zero ($\Delta U = 0$).