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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

are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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Source:  OpenStax, College physics: physics of california. OpenStax CNX. Sep 30, 2013 Download for free at http://legacy.cnx.org/content/col11577/1.1
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