Calculating Reversible Work and Irreversibility in a Filling Container

[albertov123]

Homework Statement

A rigid and evacuated container of volume V that is surrounded by atmosphere (P₀, T₀). At some point neck valve opens and atmospheric air gradually fills the container. The wall of container is thin enough so that eventually the trapped air and atm reach thermal equilibrium. The neck valve remains open, therefore at the end the trapped air and atmosphere are also in mechanical equilibrium. Calculate the reversible work and irreversibility.

Homework Equations

The Attempt at a Solution

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From the first law Q + m_inh_in = m₂u₂

Q_out = P₀.V

S_gen=Q/T=P₀.V/T₀

I = T₀S = P₀.V = I

I = W_rev - W_irrev

How can I find reversible work? I assumed work is zero in first law. But which work was that irreversible or reversible I don't know.

 

[Chestermiller]

The irreversible work is the shaft work, which you correctly determined to be zero. The reversible work is a theoretical quantity, representing the work that could have been done. The irreversibility is the lost work.