Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expansion of the gas? (b) Why or why not?

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Consider the concept of work in thermodynamics, which is defined as the energy transfer that occurs when an object is moved by a force. In the context of gases, work is often associated with a change in volume against an external pressure.

Identify the initial conditions: one flask contains gas, and the other is evacuated, meaning it has no gas and therefore no pressure.

When the valve is opened, the gas expands into the evacuated flask. Since the evacuated flask has no pressure, the gas expands freely without doing work against an external pressure.

Understand that in a free expansion, such as this one, the external pressure is zero, and therefore the work done (W) is calculated as W = P_{ext} \(\times\) \(\Delta\) V, where P_{ext} is the external pressure. Since P_{ext} = 0, the work done is zero.

Conclude that no work is performed during the expansion of the gas because the expansion occurs into a vacuum, where there is no opposing force or pressure to do work against.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Work in Thermodynamics

In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For gases, work can occur during expansion or compression when the gas exerts pressure on its surroundings. In the context of the question, understanding whether work is done during the gas expansion involves analyzing the system's boundaries and the nature of the expansion process.

Free Expansion

Free expansion refers to the process where a gas expands into a vacuum without performing work on the surroundings. In this scenario, since the gas moves from a filled flask to an evacuated one, there is no opposing pressure to work against, meaning no energy is transferred as work. This concept is crucial for determining whether work is done during the gas's expansion.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In an insulated system, the internal energy change is equal to the heat added to the system minus the work done by the system. Since there is no heat exchange and no work done during the free expansion, the internal energy of the gas remains constant, which is essential for understanding the energy dynamics in this scenario.

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