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Types of Work: Reversible & Irreversible

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

Chemical reactions can produce work. In this lesson, we will learn how this work occurs and the two types of work, reversible and irreversible. We will also compare reversible and irreversible work.

What is Work?

How does a car run? Or how does water make energy? These sources of energy occur due to the work produced by a chemical reaction. The technical definition of work is the displacement in the direction of a force. The most common equation we use to measure work is that work is equal to force times distance:

W = Fd

But in a chemical reaction, there is no displacement, there is no distance change. So how does work occur with a chemical reaction?

What is produced with exothermic reactions? Heat. In order to utilize the heat to run a piston in a car, we need to first understand that as temperature changes so does the pressure:

PV=nRT

P: pressure

V: volume

n: number of molecules

R: a constant

T: temperature

So, as the temperature from the reaction of burning gas in a car increases the pressure in a piston will also increase. And there is another equation we can use to measure work. Work is equal to the pressure times the change in volume:


Work equals pressure times volume


We can measure the change in volume when the reaction occurs in a closed system like a piston. Using this equation we can measure the work that will be done when a chemical reaction gives off heat, changing the pressure in a system.

Reversible and Irreversible Work

As we are compressing these pistons there are two options, it can be reversible or irreversible. Reversible work means that the entire system (including the surrounding system) can be returned to the starting state. Irreversible work means that we can only bring the piston back to the starting state if we change the surrounding system.

True reversible work only occurs theoretically. Let's take a look at the car piston. It gets compressed and it would seem as though it needs to go back to the original state so that it can keep running (otherwise we would only be able to use a piston once and it would never work again). So we would expect the piston to go back and forth like this:


Reversible work uses the same process, in reverse, to return to the starting position
Reversible work image


But this is saying that the piston is going back to the starting position by simply going backwards, using the exact same path as before, nothing else has been affected. In reality, the piston gives off heat, it needs to be cooled down externally. Thus increasing the heat (entropy) of the environment around it, and the system looks more like this:


Irreversible work uses a different path to return to the starting position, thus changing the surrounding environment
Irreversible work image


It does go back to the starting position, but it needs to take a new route, one where heat is given off into the environment.

Equations and Graphs

In order to calculate the work done by a reversible or irreversible process, we need to use different equations.

The equation for calculating the work done by a reversible process is:


Reversible work equation


In this situation, the pressure can be calculated directly using the ideal gas law, as given above: PV = nRT.

The 'd' refers to the derivative, so we can take the derivative of work and the derivative of volume in order to see the change over time.

The equation for calculating the work done by an irreversible process is slightly different. Just as the ideal gas law doesn't really work in reality, we need to use a different pressure to calculate the irreversible work:


Irreversible work equation


In this equation, we need to use the external pressure that is on the piston in order to calculate the work.

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