Based on the two previous answers, this is my attempt from a microscopical point of view:

• The gas near the valve acts as a "wall" against which the air inside the tyre is expanding. When particles inside the tyre "push" this "wall", they lose Kinetic Energy and they cool down. Adiabatic expansion

• The energy transferred to the particles that form the "wall" near the valve gets lost when these air molecules exit the valve. Joule effect

Thus the Kinetic Energy of the particles inside the tyre gets lower and lower --> lower temperature.

(Example 6.10 from Fundamentals of Engineering Theormodynamics by Moran)

Based on the two previous answers, this is my attempt from a microscopical point of view:

• The portion of air that happens to be near the valve acts as a "wall". The rest of the air inside the tyre "pushes" this wall out. Thus, particles inside the tyre cool down because they are transferring Kinetic Energy to the particles in the wall. Adiabatic expansion

• The particles near the valve eventually escape the tyre, so the energy that has been transfered to them also exists the tyre. Joule effect

Thus the Kinetic Energy of the particles inside the tyre gets lower and lower $\Rightarrow$ lower temperature.

(Example 6.10 from Fundamentals of Engineering Theormodynamics by Moran)

Edit: given that the particles of the gas interact (they "push" each other...) this implicitly asumes a Real Gas (not Ideal)

Based on the two previous answers, this is my attempt from a microscopical point of view:

• The gas near the valve acts as a "wall" against which the air inside the tyre is expanding. When particles inside the tyre "push" this "wall", they lose Kinetic Energy and they cool down. Adiabatic expansion

• The the energy transferred to the particles that form the "wall" near the valve gets lost when these air molecules exit the valve. Joule effect

Thus the Kinetic Energy of the particles inside the tyre gets lower and lower --> lower temperature.

Based on the two previous answers, this is my attempt from a microscopical point of view:

• The gas near the valve acts as a "wall" against which the air inside the tyre is expanding. When particles inside the tyre "push" this "wall", they lose Kinetic Energy and they cool down. Adiabatic expansion

• The energy transferred to the particles that form the "wall" near the valve gets lost when these air molecules exit the valve. Joule effect

Thus the Kinetic Energy of the particles inside the tyre gets lower and lower --> lower temperature.

(Example 6.10 from Fundamentals of Engineering Theormodynamics by Moran)