# Heat and Free Expansion

JoVE Core
Physik
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JoVE Core Physik
Heat and Free Expansion

### Nächstes Video20.5: Internal Energy

Work done by a thermodynamic system is path-dependent under all conditions.

Consider a system of two cylinders connected with a pressure valve. Initially, cylinder A is filled with an ideal gas, while cylinder B is empty

On heating cylinder A, the gas absorbs the heat, temporarily increasing the pressure inside cylinder A, which opens the pressure valve. The gas expands isothermally into cylinder B, decreasing the pressure inside cylinder A.

Considering negligible gas particles in connecting tubes, the final gas volume equals the sum of the volumes of gas in both cylinders.

Here, the work is done on the pressure valve due to the heating of the gas.

In another process, consider the same system in its initial state, insulated from its surroundings, such that no heat is exchanged.

If the valve is removed, the gas undergoes a rapid free expansion into cylinder B, eventually attaining the same final volume as in the first process.

During this expansion, no boundaries move, indicating that the work done by the gas is zero under free expansion.

## Heat and Free Expansion

The work done by a thermodynamic system depends not only on the initial and final states but also on the intermediate states—that is, on the path. Like work, when heat is added to a thermodynamic system, it undergoes a change of state, and the state attained depends on the path from the initial state to the final state. Consider an ideal gas cylinder fitted with a piston. When the cylinder is heated at a constant temperature, the gas molecules absorb energy and expand slowly in a controlled isothermal manner. This pushes the piston upwards, and gas eventually attains the final volume. Here, the work is done by the gas due to heat expansion on the piston.

The gas can also attain the same final volume through a different process. Consider a cylinder surrounded by insulating walls and divided by a thin, removable partition. The lower compartment is filled with the same amount of gas at the same temperature so that the initial state is the same as mentioned above. When the partition is removed, the gas undergoes a rapid, uncontrolled expansion, with no heat passing through the insulating walls, and reaches the same final volume as in the above case. Here, no work is done by the gas during this expansion as it does not push against anything that moves. This uncontrolled expansion of a gas into the vacuum is called a free expansion.

Experimentally, there is no temperature change under a free expansion of ideal gas. This means that the final state of the gas remains the same. The intermediate states (pressures and volumes) during the transition from the initial to the final state are entirely different in the two cases. As a result, it represents two different paths connecting the same initial and final states.