Why Pressure-Volume plots?
If you are examining heat and work, and heat engines, usually you see graphs of Pressure vs Volume. Its rarely explained.
The area on a pressure-volume graph is "work" if volume is changing, or "stored energy" if volume is constant.
How do you get area? An Integral of the pressure curve is the area under that curve, which represents work for an engine cycle. Engine cycles are usually represented as a closed curve, one curve for expanding, the other for returning to the original smallest volume. The area between the curves is the work. Its not "partly work". All the area inside the curve is work. All the area outside the curve is not work.
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Can it be quantified?
A common plot shows beginning volume as 1, and beginning pressure as 1. If we assign specific values, like 1 Atmosphere pressure is 1 on the Pressure axis, and 1 Liter is the 1 on the volume axis, one can compute the exact amount of work done. 1 Atmosphere is approximately 10 newtons per square centimeter. 1 Liter is 10 centimeter-meters. So 1 unit square of area on the graph is 10x10 or 100 newton-meters of work, or 100 joules. So work is a constant amount per unit area, no matter what gas or vapor is used.
One can also use the Beta constant to calculate energy stored in a gas in the form of heat. (Beta is Gamma minus 1, or Gamma is Beta plus 1). For Air at room temperature, 0.4 is the value of Beta. The volume swept by 1 unit is 100 Joules. If Beta is 0.4, the amount of heat stored in one unit area of Volume x Pressure, is 100/0.4 or 250 Joules. So 1 liter of air appears to contains 250 Joules of heat to maintain 1 atmosphere of pressure. (In facte this approximation breaks down at state changes.)
Note we did not mention density or temperature. If its air, and 1 liter, and 1 atmosphere of pressure, its 250 joules. If the air is half the density of standard atmosphere, then its twice the ambient temperature. If the density is 10 times normal, the temperature is 1/10th ambient. All combinations are still 250 Joules. Add another 250 Joules, the pressure doubles. Add 250 Joules plus 100 Joules to do the work of expansion, and the volume can double.
A 1 Liter Engine with a 10 to 1 compression ratio will consume about 60% of the beginning heat. On the relative scale 0.6 heat units, which converts to 0.6/0.4 or 1.5 Work Area units, or 150 Joules per stroke per Ambient Temperature multiple.
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