# Calculating Reversible Work and Irreversibility in a Filling Container

• albertov123
In summary, a rigid and evacuated container of volume V is surrounded by atmosphere (P0, T0). When a neck valve opens, atmospheric air gradually fills the container and reaches thermal equilibrium with the trapped air. The valve remains open, leading to mechanical equilibrium between the trapped air and atmosphere. The reversible work and irreversibility can be calculated using the first law of thermodynamics and the formula for entropy generation. The work done is zero, representing the irreversible work, while the lost work is the difference between the reversible and irreversible work.
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.

## The Attempt at a Solution

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From the first law Q + minhin = m2u2

Qout = P0.V

Sgen=Q/T=P0.V/T0

I = T0S = P0.V = I

I = Wrev - Wirrev

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.

Last edited:
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.

## What is reversible work?

Reversible work is the maximum amount of work that can be extracted from a system while it undergoes a reversible process, where no energy is lost to the surroundings.

## How is reversible work calculated?

Reversible work can be calculated using the formula W = -RTln(K), where W is the reversible work, R is the gas constant, T is the temperature, and K is the equilibrium constant.

## What is the difference between reversible and irreversible work?

The main difference between reversible and irreversible work is that reversible work can be completely converted into useful energy, while irreversible work results in some energy being lost to the surroundings.

## What are some examples of reversible work?

A few examples of reversible work include a perfectly insulated piston expanding or compressing in a cylinder, a reversible chemical reaction, and a reversible phase change.

## Why is calculating reversible work important in science?

Calculating reversible work is important in science because it helps us understand the maximum potential of a system and how much useful energy can be extracted from it. This information is crucial in many fields, such as thermodynamics, chemistry, and engineering.

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