Work in Thermodynamics

Why does steam make things move? Why will an aerosol explode violently when left in a hot car? The simple answer: Thermodynamics is interesting! Heat as energy is complex enough to need its entire branch of physics just to explain its relationship with other energies! Thermodynamics also describes how heat acts in a system, and how its energy transfers into other forms of energy. Work in thermodynamics is, therefore, an interesting topic too, but just how does it... work? What variables do we need to look out for, and what is a thermodynamic process? Let's find out.

The Definition of Work in Thermodynamics

We usually think of work in the mechanical sense, where energy is transferred from one place to another through a force. We can also think of this concept in terms of thermodynamics, where energy in a thermodynamic system is transferred into another thermodynamic system.

Work in the field of physics is defined as the energy that is transferred when a force exerts on an object with mass over a certain distance.

Before we go a bit deeper into work in terms of thermodynamics, let's first look at thermodynamics as a whole, and what exactly it is. Thermodynamics is an entire section of physics that involves heat. Specifically, how heat interacts and transfers between other different kinds of energy, and overall the relationship heat has with all forms of energy. We know that work is energy transference, and in thermodynamics, work is only ever done in the mechanical sense.

Work in Thermodynamics Processes

So we now know how work relates in terms to thermodynamics, but what is a thermodynamic process? A thermodynamic process is quite simply the kind of way work can be done between thermodynamic systems. A thermodynamic system is a confined space with matter inside in which thermodynamic processes will take place. There are at minimum a handful of variables to take into consideration in a thermodynamic system, even more so in the transference of energy between two or more. The changes in these variables as work is done are what differentiates one thermodynamic process from another. Let's look at a few different thermodynamic processes in the context of a gas as our thermodynamic system.

An adiabatic process occurs when the only energy transferred to or from a system is via work done on or by the system. Energy is transferred outward for gas doing work and energy is transferred into the gas when external work is done on it.

An isobaric process occurs when the pressure of the gas in a system is constant. Most often, chemical reactions will take place at constant pressure, making them isobaric processes.

An isochoric process occurs when the volume of gas in a thermodynamic system is constant. Gases burnt in a car's engine are a good example of an isochoric process. These gases usually change in temperature and pressure but their volume is constant.

An isothermal process, as this pattern goes, will in turn be a system in which the temperature of the gas is constant. Melting ice remains at a constant temperature and is an example of an isothermal process.

Useful Work in Thermodynamics

Before we cover what useful work in thermodynamics is, let's first go over what useful work is. Useful work is described as the portion of work done that directly transfers useful energy. A contrast to this is the waste work done. In a system, there will always be some energy that is dissipated in another form, that is to say, there will never be a perfect transfer of 100% useful energy. The work done that is associated with this transfer of waste energy is waste work done.

So, useful work in thermodynamics can be quite simply described as the useful output from a thermodynamic system, the difference between the input work in the system, and the waste work.

\(\mathrm{Useful\:work=Total\:work - Waste\:work}\)

The Formula for Work in Thermodynamics

Work occurs in many different senses, as we have gone over. This means that many different equations are used to calculate for work. In a thermodynamic system, however, this formula is the most used and most widely applicable:

\(W=\Delta U-Q\)

Where \(W\) is the work done on or by a system, \(Q\) is the heat that enters or leaves a system, and \(\Delta U\) is the change in the internal energy of a system. The formula above is the mathematical expression of the first law of thermodynamics. This equation defines all of these variables and their relationship to one another in a thermodynamic system. For example, we now know that if we wish for thermodynamic work to remain constant, and the internal energy declines, we must then increase the amount of heat entering the system.

An arguably equally as important concept in terms of thermodynamic work is the relationship between pressure and volume in a thermodynamic system. These variables are used directly in solving for work, as shown here:

\(W=-P\Delta V\)

Where \(P\) is the pressure externally acting on the system, and \(\Delta V\) is the change in volume as it is doing work. If the system does work externally \(W<0\) and if an external force does work on the system then \(W>0\). Note that this method only works for an isobaric process with constant pressure \(P\). Essentially, the work done on a system at constant pressure, in which the volume is changing, is the area under a \(P-V\) graph. This is illustrated by the graph below.

The area under a graph of P vs V is the work done by a thermodynamic system at constant pressure, Wikimedia Commons CC BY-SA 4.0

Work in Thermodynamics Examples

Now that we've seen what equations are used to calculate work done in a thermodynamic system, let's try putting them into practice.