Final answer:
The area under a pressure-volume graph represents the work done in an isobaric process, per the equation W = PΔV. This is specific to constant pressure scenarios and is demonstrated in PV diagrams. Boyle's Law explains the inverse proportionality of pressure and volume.
Step-by-step explanation:
The question Is the area under a pressure-volume (PV) graph the same as pressure times volume? relates to the principles of thermodynamics in physics. When considering an isobaric process - a process at constant pressure - the area under a PV graph indeed represents the work done by the gas.
This is denoted by the equation W = PΔV, where W is work, P is the constant pressure, and ΔV is the change in volume. The equation PΔV is valid specifically for isobaric processes as shown in Figure 15.11. However, this should not be confused with the product of pressure and volume in general, which is only the same as area under the curve for isobaric processes.
Robert Boyle's experiment, as shown in figures referencing Boyle's work, demonstrates an inverse relationship between pressure and volume.
When graphed as volume versus 1/pressure, the resulting plots show a linear relationship, indicative of Boyle's Law, which states that at constant temperature for a fixed mass, the absolute pressure and the volume of a gas are inversely proportional.
This law is mathematically expressed as P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume, respectively.