Heat and Free Expansion

Work done by a thermodynamic system is path-dependent because it depends on the intermediate states the gas passes through, not just the initial and final states. During isothermal expansion, gas pushes against a piston, doing work. During free expansion into a vacuum, no work occurs because the gas encounters no resistance. Both processes reach the same final volume, but the work differs due to different paths.

During free expansion, a gas rapidly expands into a vacuum through a removed partition without heat exchange or boundary movement. No work is done because the gas does not push against anything that moves. For an ideal gas, the temperature remains unchanged during free expansion, meaning the final state is identical to that reached through controlled isothermal expansion.

Isothermal expansion occurs when a heated gas slowly expands against a movable piston at constant temperature, doing work on the piston. Free expansion occurs when a gas rapidly expands into a vacuum with no heat exchange and no work done. Both processes connect the same initial and final states but follow entirely different paths with different intermediate pressures and volumes.

Yes, two different thermodynamic processes can connect identical initial and final states while following different paths. In this video, isothermal expansion and free expansion both result in the same final volume and temperature for an ideal gas. However, the intermediate states—pressures and volumes during transition—differ completely between the two paths.

The pressure valve opens when heating increases gas pressure inside cylinder A, allowing controlled isothermal expansion into cylinder B. The valve maintains pressure equilibrium between cylinders as gas flows through. This controlled mechanism enables work to be done on the valve, contrasting with free expansion where no valve exists and no work occurs.

During free expansion, an ideal gas undergoes rapid, uncontrolled expansion into a vacuum with insulating walls preventing heat exchange. Since no work is done and no heat is transferred, the internal energy remains constant. For an ideal gas, internal energy depends only on temperature, so constant internal energy means temperature remains unchanged.

The first law states that internal energy change equals heat added minus work done. During free expansion, no heat is exchanged and no work is performed, so internal energy change is zero. This explains why an ideal gas maintains constant temperature during free expansion, demonstrating that the first law thermodynamics problem solving requires careful analysis of both heat and work terms.