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W = P Δ V  (isobaric process). size 12{W=PΔV} {}

Note that if Δ V size 12{ΔV} {} is positive, then W size 12{W} {} is positive, meaning that work is done by the gas on the outside world.

(Note that the pressure involved in this work that we’ve called P size 12{P} {} is the pressure of the gas inside the tank. If we call the pressure outside the tank P ext size 12{P rSub { size 8{"ext"} } } {} , an expanding gas would be working against the external pressure; the work done would therefore be W = P ext Δ V size 12{W= - P rSub { size 8{"ext"} } ΔV} {} (isobaric process). Many texts use this definition of work, and not the definition based on internal pressure, as the basis of the First Law of Thermodynamics. This definition reverses the sign conventions for work, and results in a statement of the first law that becomes Δ U = Q + W size 12{ΔU=Q+W} {} .)

It is not surprising that W = P Δ V size 12{W=PΔV} {} , since we have already noted in our treatment of fluids that pressure is a type of potential energy per unit volume and that pressure in fact has units of energy divided by volume. We also noted in our discussion of the ideal gas law that PV size 12{ ital "PV"} {} has units of energy. In this case, some of the energy associated with pressure becomes work.

[link] shows a graph of pressure versus volume (that is, a PV size 12{ ital "PV"} {} diagram for an isobaric process. You can see in the figure that the work done is the area under the graph. This property of PV size 12{ ital "PV"} {} diagrams is very useful and broadly applicable: the work done on or by a system in going from one state to another equals the area under the curve on a PV size 12{ ital "PV"} {} diagram .

The graph of pressure verses volume is shown for a constant pressure. The pressure P is along the Y axis and the volume is along the X axis. The graph is a straight line parallel to the X axis for a value of pressure P. Two points are marked on the graph at either end of the line as A and B. A is the starting point of the graph and B is the end point of graph. There is an arrow pointing from A to B. The term isobaric is written on the graph. For a length of graph equal to delta V the area of the graph is shown as a shaded area given by P times delta V which is equal to work W.
A graph of pressure versus volume for a constant-pressure, or isobaric, process, such as the one shown in [link] . The area under the curve equals the work done by the gas, since W = P Δ V size 12{W=PΔV} {} .
The diagram in part a shows a pressure versus volume graph. The pressure is along the Y axis and the volume is along the X axis. The curve is a smooth falling curve from the highest point A to the lowest point B. The curve is segmented into small vertical rectangular sections of equal width. One of the sections is marked as width of delta V sub one along the X axis. The pressure P sub one average multiplied by delta V sub one gives the work done for that strip of the graph. Part b of the figure shows a similar graph for the reverse path. The curve now slopes upward from point A to point B. An equation in the top right of the graph reads W sub in equals the opposite of W sub out for the same path.
(a) A PV size 12{ ital "PV"} {} diagram in which pressure varies as well as volume. The work done for each interval is its average pressure times the change in volume, or the area under the curve over that interval. Thus the total area under the curve equals the total work done. (b) Work must be done on the system to follow the reverse path. This is interpreted as a negative area under the curve.

We can see where this leads by considering [link] (a), which shows a more general process in which both pressure and volume change. The area under the curve is closely approximated by dividing it into strips, each having an average constant pressure P i ( ave ) size 12{P rSub { size 8{i \( "ave" \) } } } {} . The work done is W i = P i ( ave ) Δ V i size 12{W rSub { size 8{i} } =P rSub { size 8{i \( "ave" \) } } DV rSub { size 8{i} } } {} for each strip, and the total work done is the sum of the W i size 12{W rSub { size 8{i} } } {} . Thus the total work done is the total area under the curve. If the path is reversed, as in [link] (b), then work is done on the system. The area under the curve in that case is negative, because Δ V size 12{ΔV} {} is negative.

PV size 12{ ital "PV"} {} diagrams clearly illustrate that the work done depends on the path taken and not just the endpoints . This path dependence is seen in [link] (a), where more work is done in going from A to C by the path via point B than by the path via point D. The vertical paths, where volume is constant, are called isochoric processes. Since volume is constant, Δ V = 0 size 12{ΔV=0} {} , and no work is done in an isochoric process. Now, if the system follows the cyclical path ABCDA, as in [link] (b), then the total work done is the area inside the loop. The negative area below path CD subtracts, leaving only the area inside the rectangle. In fact, the work done in any cyclical process (one that returns to its starting point) is the area inside the loop it forms on a PV size 12{ ital "PV"} {} diagram, as [link] (c) illustrates for a general cyclical process. Note that the loop must be traversed in the clockwise direction for work to be positive—that is, for there to be a net work output.

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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s. Reply
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Devang Reply
are you nano engineer ?
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
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abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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Ramkumar Reply
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Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
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I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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Mykayuh Reply
Because I'm writing a report and I would like to be really precise for the references
Gre Reply
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!
Gre Reply
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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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