QJEEM24Chdab3: JEE Main 2024 Chemistry - Class 11 JEEM24Chdab3 Solution: Choose the correct option for free expansion of an ideal gas…

Let's analyze what happens during a free (or unrestrained) expansion of an ideal gas under adiabatic conditions:

• Adiabatic process : By definition, in an adiabatic process, no heat is transferred between the system and its surroundings. Thus, $q = 0$ .


• Free expansion : In a free expansion, the gas expands into a vacuum or against zero external pressure. Since work ( $w$ ) is defined as the product of pressure ( $P$ ) and volume change ( $\Delta V$ ), and since the external pressure is zero, we conclude that $w = 0$ .


• Temperature change ( $\Delta T$ ) : Since work is zero and no heat is transferred, the first law of thermodynamics tells us that the change in internal energy ( $\Delta U$ ) is zero as well. For an ideal gas, internal energy is a function of temperature only; thus, if the internal energy does not change, the temperature does not change. Therefore, $\Delta T = 0$ .

Based on the above points, the free expansion of an ideal gas under adiabatic conditions is characterized by no heat transfer ( $q = 0$ ), no work done ( $w = 0$ ), and no change in temperature ( $\Delta T = 0$ ). Therefore, the correct option is:

Option A : $q = 0, \Delta T = 0, w = 0$