Isobaric Processes: Definition, Formula & Examples

Several idealized thermodynamic processes describe how states of an ideal gas can undergo change. The isobaric process is just one of these.

What Is the Study of Thermodynamics?

Thermodynamics is the study of changes that occur in systems due to the transfer of thermal energy (heat energy). Any time two systems of different temperature are in contact with each other, heat energy will transfer from the hotter system to the cooler system.

Many different variables affect how this heat transfer occurs. The molecular properties of the materials involved affect how quickly and easily heat energy is able to move from one system to another, for example, and the specific heat capacity (the amount of heat required to raise a unit mass by 1 degree Celsius) affects the resulting final temperatures.

When it comes to gases, many more interesting phenomena occur when heat energy is transferred. Gases are able to expand and contract significantly, and how they do so depends on the container they are confined in, the pressure of the system and the temperature. Understanding how gases work, therefore, is important in understanding thermodynamics.

Kinetic Theory and State Variables

Kinetic theory provides a way of modeling a gas so that statistical mechanics can be applied, eventually resulting in being able to define a system via a set of state variables.

Consider what a gas is: a bunch of molecules all able to move freely around each other. In order to understand a gas, it makes sense to look at its most basic components – the molecules. But not surprisingly, this becomes cumbersome very quickly. Imagine the sheer number of molecules in just a glass full of air for example. There is not a computer powerful enough to keep track of the interactions of that many particles with each other.

Instead, by modeling the gas as a collection of particles all undergoing random motion, you can begin to understand the overall picture in terms of root mean square velocities of the particles, for example. It becomes convenient to begin speaking of the average kinetic energy of the molecules instead of identifying the energy associated with each individual particle.

These quantities lead to the ability to define state variables, which are quantities that describe the state of a system. The main state variables discussed here will be pressure (the force per unit area), volume (the amount of space the gas takes up) and temperature (which is a measure of the average kinetic energy per molecule). By studying how these state variables relate to each other, you can gain an understanding of thermodynamic processes on a macroscopic scale.

Charles’ Law and the Ideal Gas Law

An ideal gas is a gas in which the following assumptions are made:

The molecules can be treated like point particles, taking up no space. (For this to be the case, high pressure is not allowed, or the molecules will become close enough together that their volumes become relevant.)

Intermolecular forces and interactions are negligible. (Temperature cannot be too low for this to be the case. When temperature is too low, the intermolecular forces start to play a relatively larger role.)

The molecules interact with each other and the walls of the container in perfectly elastic collisions. (This allows for the assumption of conservation of kinetic energy.)

Once these assumptions are made, some relationships become apparent. Among these are the ideal gas law, which is expressed in equation form as:

PV = nRT = NkT

Where P is pressure, V is volume, T is temperature, n is the number of moles, N is the number of molecules, R is the universal gas constant, k is the Boltzmann constant and nR = Nk.

Closely related to the ideal gas law is Charles’ law, which states that, for constant pressure, the volume and temperature are directly proportional, or V/T = constant.

What Is an Isobaric Process?

An isobaric process is a thermodynamic process that occurs at constant pressure. In this realm, Charles’ law applies since pressure is held constant.

The types of processes that can happen when pressure is held constant include isobaric expansion, in which volume increases while temperature decreases, and isobaric contraction, in which volume decreases while temperature increases.

If you’ve ever cooked a microwave meal that requires you to cut a vent in the plastic before putting it in the microwave, this is because of isobaric expansion. Inside the microwave, the pressure inside and outside the plastic-covered meal tray is always the same and always in equilibrium. But as the food cooks and heats up, the air inside the tray expands as a result of the increase in temperature. If no vent is available, the plastic might expand to the point where it bursts.

For a quick at-home isobaric compression experiment, put an inflated balloon in your freezer. Again, pressure inside and outside the balloon will always be in equilibrium. But as the air in the balloon cools, it will shrink as a result.

If whatever container the gas is in is free to expand and contract, and the external pressure remains constant, then any process will be isobaric because any difference in pressures would cause expansion or contraction until that difference is resolved.

Isobaric Processes and the First Law of Thermodynamics

The first law of thermodynamics states that the change in internal energy U of a system is equal to the difference between the amount of heat energy added to the system Q and net work done by the system W. In equation form, this is:

\Delta U = Q - W

Recall that temperature was the average kinetic energy per molecule. The total internal energy is then the sum of the kinetic energies of all of the molecules (with an ideal gas, potential energies are considered negligible). Hence internal energy of the system is directly proportional to temperature. Because the ideal gas law relates pressure and volume to temperature, the internal energy is also proportional to the product of pressure and volume.

So if heat energy is added to the system, the temperature increases as does the internal energy. If the system does work on the environment, then that amount of energy is lost to the environment, and the temperature and internal energy decrease.

On a PV diagram (graph of pressure vs. volume), an isobaric process looks like a horizontal line graph. Since the amount of work done during a thermodynamic process is equal to the area under the PV curve, the work done in an isobaric process is simply:

W = P\Delta V

Isobaric Processes in Heat Engines

Heat engines convert heat energy into mechanical energy via a complete cycle of some sort. This typically requires a system to expand at some point during the cycle in order to do work and impart energy to something external.

Consider an example in which an Erlenmeyer flask is connected via plastic tubing to a glass syringe. Confined within this system is a fixed amount of air. If the plunger of the syringe is free to slide, acting as a movable piston, then by placing the flask in a heat bath (a tub of hot water), the air will expand and lift the plunger, doing work.

To complete the cycle of such a heat engine, the flask would need to be placed in a cold bath so that the syringe can return to its starting state again. You can add an additional step of having the plunger be used to lift a mass or do some other form of mechanical work as it moves.

Other Thermodynamic Processes

Other processes discussed in more detail in other articles include:

Isothermal processes, in which temperature is held constant. At constant temperature, pressure is inversely proportional to volume, and isothermal compression results in an increase in pressure while isothermal expansion results in a decrease in pressure.

In an isochoric process, volume of the gas is held constant (the container holding the gas is held rigid and unable to expand or contract). Here pressure is then directly proportional to temperature. No work can be done on or by the system since the volume does not change.

In an adiabatic process, no heat is exchanged with the environment. In terms of the first law of thermodynamics, this means Q = 0, hence any change in internal energy directly corresponds to work being done on or by the system.

References

About the Author

Gayle Towell is a freelance writer and editor living in Oregon. She earned masters degrees in both mathematics and physics from the University of Oregon after completing a double major at Smith College, and has spent over a decade teaching these subjects to college students. Also a prolific writer of fiction, and founder of Microfiction Monday Magazine, you can learn more about Gayle at gtowell.com.