Why the temperature of the gas falls during its expansion which owes to the change in pressure only? It is said everywhere that when gas is allowed to expand enough slowly it temperature falls but the system keep adjusting its temperature at a single value by absorbing heat from reservoir continiously. 
Text in both of the following photos suggest it.
From wikipedia:

From textbook:

Why does the temperature of the system (gas) fall when gas expands owing to the reduction of pressure?
What is its explanation at molecular level?
 A: First, macroscopically, when a volume of gas expands, it pushes against the gas surrounding it, and so does work against that surrounding gas. Thus, the expanding gas loses momentum and energy to its surrounding environment, which corresponds to a decrease in temperature (a la $\frac12kT$ energy per degree of freedom).
Microscopically, at the surface of the expanding gas, molecules inside the volume collide with molecules outside. And net energy is transferred out precisely corresponding to the fact that the volume expands. And that, in turn, corresponds to the fact that $T_{inside}>T_{outside}$, i.e., the inside molecular speed is, on average, greater than the outside speed, so average collisions transfer momentum (and energy) from inside to outside.
In comparison, suppose the volume of gas were expanding into a vacuum, so there are no collisions with outside molecules. That's called a throttling process. And guess what? -- no collisions, so no energy transfer outside the volume, and therefore no temperature change (at least not for an ideal gas).
