I was watching a video from mitocw in which the professor wrote that:
dU = dw(reversible)
If we consider a free expansion, then the work done must be 0. The process is also adiabatic implying that heat transferred must also be 0.
Now we know that Temperature of the gas would change (as pressure would decrease) but the change in the internal energy would be 0. The fact that temperature is changing without bringing about a change in internal energy is something i am unable to understand.
It sounds like you are describing a throttling process, as occurs with the use of a throttling valve between the output of a condenser and input of an evaporator in a refrigeration cycle. The process is considered adiabatic, and constant temperature (change in internal energy = 0) and the product of pressure and volume is a constant. A drop in pressure is coupled with an increase in volume so that PV=constant. Since a change in enthalpy (h) equals a change in internal energy (u) + a change in PV, the change in enthalpy is 0. Bottom line- everything you said is true except that there is no change in temperature, per Chester Miller's comment. Hope this helps.
Bob D has already answered about the throttling process, which is isothermal and is considered adiabatic. But i think your question was about free expansion of gas. Consider an adiabatic chamber with a removable partition, with one half containing ideal gas and the other half being vacuum, now when the partition is removed the pressure drops, volume increases but temperature remains same. Here's why, as you said that w=0 for free expansion, and when q=0, then according to Ist Law ΔU = 0. Since for an ideal gas internal energy is a function of its temperature only, therefore if internal energy does not change, then temperature must also not change.
Also, the throttling process is isothermal for ideal gases and not real gases. For real gases temperature would increase or decrease depending upon which side of the inversion curve, does the state of the gas lie before throttling.
