Prove that free expansion of a gas is irreversible. Consider a perfect insulatin

ID: 3280776 • Letter: P

Question

Prove that free expansion of a gas is irreversible. Consider a perfect insulating tank with a barrier that allows one compartment to hold a gas (at p_0, V_0, T_0) While the other, equal volume, compartment is evacuated (call this state 0). Free expansion occurs when the barrier is ruptured and the gas fills both compartments (call this state 1 after it has occurred). In this process, W=0, Q=0, Assume it is reversible, that the gas transitions from state 1 to state 0. From state 0 set up a cycle extracting work, while only relying on a single heat reservoir to return it back to state 1. Draw a qualitative PV diagram of the process and comment on the efficiency and why it must be irreversible.

Explanation / Answer

'Free expansion' as an irreversible process

Well, before answering the question, I want to recall “What is meant by IRREVERSIBLE PROCESS”

For reversible process, Thermodynamic State of SYSTEM as well as SURROUNDING before and after the process must remain same.

Both conditions (of system & surrounding) should satisfy simultaneously.

Having same state of system before and after process doesn’t guarantee the process to be reversible, we must check also about surrounding.

SYSTEM: control mass (fixed mass of gas within boundary)

SURROUNDING: Everything outside boundary of control mass.

Here while expansion of gas, there is no opposing pressure force (i.e free expansion) . Expansion in empty space.

Since no opposing pressure force means no work done by gas while expansion .

Surrounding experiencing nothing during expansion process,no work involve across boundary. Consequent it’s state remain as it is .

AFTER THE EXPANSION PROCESS TOOK PLACE

NOW, if we want to get back system to its original state, we have to disturb surrounding. System can't get back to its original state automatically we must work on it. Result in change in surrounding.

CONCLUSION: though system having same state before and after process, surrounding doesn’t!! I.e. Process is IRREVERSIBLE

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Prove that free expansion of a gas is irreversible. Consider a perfect insulatin

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