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,
, 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
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.
(a) The work done in going from A to C depends on path. The work is greater for the path ABC than for the path ADC, because the former is at higher pressure. In both cases, the work done is the area under the path. This area is greater for path ABC. (b) The total work done in the cyclical process ABCDA is the area inside the loop, since the negative area below CD subtracts out, leaving just the area inside the rectangle. (The values given for the pressures and the change in volume are intended for use in the example below.) (c) The area inside any closed loop is the work done in the cyclical process. If the loop is traversed in a clockwise direction,
is positive—it is work done on the outside environment. If the loop is traveled in a counter-clockwise direction,
is negative—it is work that is done to the system.
Total work done in a cyclical process equals the area inside the closed loop on a
PV Diagram
Calculate the total work done in the cyclical process ABCDA shown in
[link] (b) by the following two methods to verify that work equals the area inside the closed loop on the
diagram. (Take the data in the figure to be precise to three significant figures.) (a) Calculate the work done along each segment of the path and add these values to get the total work. (b) Calculate the area inside the rectangle ABCDA.
Strategy
To find the work along any path on a
diagram, you use the fact that work is pressure times change in volume, or
. So in part (a), this value is calculated for each leg of the path around the closed loop.
Solution for (a)
The work along path AB is
Since the path BC is isochoric,
, and so
. The work along path CD is negative, since
is negative (the volume decreases). The work is
Again, since the path DA is isochoric,
, and so
. Now the total work is
Solution for (b)
The area inside the rectangle is its height times its width, or
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
Got questions? Join the online conversation and get instant answers!
