Chapter4, Lesson A - Quasi-Equilibrium Expansion of a Gas

4A-5 :	Quasi-Equilibrium Expansion of a Gas								4 pts

Estimate the work done by a gas during an unknown process. Data obtained that relates pressure and volume are :

	P (kPa)	200	250	300	350	400	450	500
	V (cm3)	800	650	550	475	415	365	360


Read :	The key concept here is that boundary or PV work is represented by the area under the process path curve on a PV Diagram. So, once we plot the given data on a PV Diagram, all we need to do is numerically integrate to determine the area under the curve and we will have the work !



Given:	P (kPa)	V (L)
	200	0.800
	250	0.650
	300	0.550
	350	0.475
	400	0.415
	450	0.365
	500	0.360



Find:	W	???	J




Assumptions:		- Each state in the data table is an equilibrium state.
		- The process is a quasi-equilibrium process.
		- The system is a closed system.
		- The trapezoidal rule gives an acceptable estimate of the area under the process path in the PV Diagram.


Solution :	The area of each trapezoid under the process path in the PV Diagram is the product of the average pressure for that trapezoid and the change in volume across the trapezoid.


	Trapezoid	Pavg (kPa)	ΔV (L)	W (J)
	A	475	-0.005	-2
	B	425	-0.050	-21
	C	375	-0.060	-23
	D	325	-0.075	-24
	E	275	-0.100	-28
	F	225	-0.150	-34

Answer:	Wtotal =	-132	J

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