Q1: No cooling occurs, when an ideal gas undergoes unrestrained expansion, because the molecules

ANS:C - are above the inversion temperature.

The correct statement is: "do work equal to loss in kinetic energy." When an ideal gas undergoes unrestrained expansion, it expands into a vacuum, meaning there's no external pressure to do work against. In this process, the gas molecules are doing work to expand against the vacuum. According to the first law of thermodynamics, the change in internal energy (Δ𝑈ΔU) of the gas is equal to the heat added (𝑄Q) to the gas minus the work done (𝑊W) by the gas: Δ𝑈=𝑄−𝑊ΔU=Q−W Since no heat is added or removed in this unrestrained expansion process, 𝑄=0Q=0. And since the gas is expanding against zero external pressure, the work done by the gas is also zero (𝑊=0W=0). Therefore, the change in internal energy is zero (Δ𝑈=0ΔU=0). In an ideal gas, the internal energy is solely a function of the temperature. If the change in internal energy is zero (Δ𝑈=0ΔU=0), it implies that there's no change in temperature. So, no cooling occurs during unrestrained expansion of an ideal gas because the gas molecules do work equal to the loss in their kinetic energy, maintaining the internal energy and thus the temperature constant.