Isobar (pressure)

The PV diagram of an isobaric process

An isobar in the context of thermodynamics refers to any process in which the system remains at a constant (unchanging) pressure throughout.

When a system expands at a constant pressure, such as a piston in an internal combustion engine, its volume is increasing and this corresponds to an output of work. However, the system cannot do this work without an input (or output) of heat. By analyzing the first law of thermodynamics, the amount of heat necessary to do a given amount of work without the pressure changing can be calculated by using the system's specific heat capacity.

To calculate the work done in an isobaric process, simply calculate the negative area under the curve. This is calculated using the ideal gas law the following equation:

[math]W = -p\Delta V[/math]

Therefore, a closed system that is being compressed (decreasing volume), will have a positive [math]W[/math] value—contrarily an expansion (increasing volume) will result in a negative [math]W[/math] value. For a system to compress, it requires a cooling source (or output of heat from the system) to keep the pressure constant. Otherwise, the compressed volume without the removal of heat will increase the pressure. Contrarily, for expansion the system requires an input of heat, otherwise without the addition of heat, the pressure in the container would decrease.

A real life example where an isobaric process is taking place is when cooking food. Since the pot is an open system, the molecules can escape (as vapour) as the contents in the pot get hotter. Referring to the ideal gas law: [math]pV = nRT[/math], if heat is added to this system temperature ([math]T[/math]) increases, however, since it's an open system, molecules can escape ([math]n[/math] decreases). When molecules escape this will decrease the volume ([math]V[/math]) as well.

To think of it through values imagine that pressure ([math]p[/math]) is 6, [math]V[/math] is 10, [math]n[/math] is 3, and [math]T[/math] is 20 (R is just a constant). Currently, both equations are equal to one another with the value of 60. The cooking will cause [math]T[/math] to be 25 and [math]n[/math] to be 2. Therefore, volume needs to decrease a bit (8.3), so then pressure can stay constant.

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For Further Reading

• PV diagram
• Ideal gas law
• Isochore
• Isothermal
• Adiabatic
• System and surrounding
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