The graphical nature of pressure volume work, signified by the area of region abcd, was conceived when in the 1830s French physicist Emile Clapeyron began to use the indicator diagram, invented in 1796 by Scottish engineer James Watt and his employee John Southern, to quantify the mechanical work of the steam. |

δW = PdV

whereby upon integration of the definite integral:

equates to:

W = PΔV = P (Vf – Vi)whereby the system pressure and initial and final volume give solution to the calculation of pressure volume work.

A 2011 derivation overview of pressure volume work, with a human example application from the 2004 film Mean Girls, by Libb Thims. |

To derive the equation for pressure volume work, we start with the standard definition of pressure, loosely deriving from Dutch-born Swiss physicist Daniel Bernoulli’s 1738 bookSee main: dW = PdV

whereby

F = PA

We then substitute this into French physicist Gustave Coriolis' 1829 principle of the transmission of work:

W = Fd

where mechanical work

W = (PA)d

In the case of a geometric body of a piston and cylinder, as shown adjacent, the area

W = PV

or in Neumann notation:

đW = PdV

where the d-crossbar đ derivative signifies that the work in this case is an inexact derivative.

History

The general formulation of pressure volume work was introduced in 1834 by French physicist Emile Clapeyron. [1]

References

1. Clapeyron, Émile. (1834). “Memoir on the Motive Power of Heat”,

External links

● Pressure-volume work – Wikipedia.

● Pressure volume work – CityCollegiate.com.