Question

how does the ke from the water bath outside the closed jar get to the air particles inside the closed jar

Answer 1

Short answer: by heat transfer across the jar wall — the water warms the jar material, that warmth is transmitted through the solid wall (by atomic vibrations / conduction and by radiation), and the inner surface then transfers energy to the gas by collisions. The gas molecules gain kinetic energy when they collide with the warmed inner surface (and then share it by colliding with each other).

Step-by-step microscopic picture
- Water molecules near the outside surface hit and interact with the jar’s outer atoms, raising the vibrational energy of those atoms (they get “hotter”).
- In the solid wall that vibrational energy travels inward as lattice vibrations (phonons) and/or via electronic heat conduction depending on the material.
- The inner surface atoms vibrate more and collide electromagnetically with gas molecules that hit the wall, transferring some energy to those gas molecules (increasing their kinetic energy).
- Those warmed gas molecules then bump into other gas molecules and spread the energy by convection/diffusion inside the jar.

Other routes
- Thermal radiation: a warm object emits infrared photons. Some of that radiative energy can pass into the jar cavity and be absorbed by the inner surface or gas molecules.
- If the jar interior were a vacuum, there would be no gas conduction, but energy still reaches the cavity by conduction through the wall and by radiation.

What controls how fast this happens
- Thermal conductivity and thickness of the wall, temperature difference, surface area, and whether the jar material transmits infrared. Metal transfers heat fast; glass and plastic are slower; insulating materials are slowest.

In short, energy doesn’t “jump” through the closed jar — it is passed along by interactions at the boundary: solids conduct the energy across the wall, and collisions/radiation deliver it to the air inside.