Does Air Entering an Evacuated Bottle Perform Work?

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When air enters an evacuated bottle upon opening, work is indeed done by the air, contrary to the notion of no work during free expansion. The system can be defined as the volume of air entering the bottle, which experiences changes in pressure and volume. The equation W=∫PdV is applicable primarily to quasi-equilibrium processes, but some work occurs in non-quasi-equilibrium situations as well, such as in accelerating the air and overcoming drag. The discussion highlights the complexities of defining work in dynamic processes. Understanding these nuances is essential for accurate thermodynamic analysis.
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When air enters into an evacuated bottle from atmosphere when the cork is opened, is there any work done by the air? My textbook says that there is , but i thought no work was done during free expansion?
Consider the amount of air entering as the system.
Moreover, is W=∫PdV applicable only for quasi eqbm process or all processes?
 
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Some work is done in accelerating the air and in overcoming drag in the neck of the bottle. But whether that's what the textbook author had in mind I've no idea.
 

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