Keeping a System at Constant Pressure: The Isobaric Process

In physics, when you have a process where the pressure stays constant, it’s called isobaric (baric means “pressure”). The first figure shows an example of an isobaric system, where a cylinder with a piston is being lifted by a quantity of gas as the gas gets hotter. The volume of the gas is changing, but the weighted piston keeps the pressure constant.

An isobaric system may feature a change in volume, but the pressure remains constant.
An isobaric system may feature a change in volume, but the pressure remains constant.

Graphically, you can see what the isobaric process looks like in the second figure, where the volume is changing while the pressure stays constant. Because 


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the work is the shaded area beneath the graph.

Pressure and volume in an isobaric system.
Pressure and volume in an isobaric system.

Say you have 60 cubic meters of an ideal gas at a pressure of 200 pascals. You heat the gas until it expands to a volume of 120 cubic meters. How much work does the gas do? All you have to do is plug in the numbers:

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The gas does 12,000 joules of work as it expands under constant pressure.

Here’s another example: Suppose you’re waiting for a connecting flight to the next physics conference. You look around but don’t see much to amuse yourself with — just a water fountain. Proving that physicists can find fun anywhere, you take a gram of water from the fountain and put it into the pocket isobaric chamber that you always happen to carry with you. As an airport security guard looks on, you increase the pressure to

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and increase the temperature of the water by 62 degrees Celsius.

You note that the gram of water increases in volume by

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“Hmm,” you think. “I wonder what work was done by the water and what the change in internal energy of the water was.” The process was isobaric, so the work done by the water was

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Filling in the numbers and doing the math yields:

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So that’s the work done by the water. What about the change in the internal energy of the water? The first law of thermodynamics tells you that

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You know W, but what is Q? Q is the heat absorbed by the water. You know the change in temperature of the water, and using the water’s specific heat capacity, you can find the heat actually absorbed by the water using this equation:

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numbers and doing the math gives you

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Now back to the first law of thermodynamics:

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Substituting in the values gives you the change in internal energy:

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Hmm, you think. The work done was a tiny 0.002 joules, while the change in internal energy was 260 joules. Interesting — very little work was done because the water didn’t expand much, but you saw a fair gain in internal energy because the water’s temperature went up.

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