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Welcome to our Physics lesson on **Finding Work using a P - V Diagram**, this is the fifth lesson of our suite of physics lessons covering the topic of **The Kinetic Theory of Gases. Ideal Gases**, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

It is clear that in a P - V diagram, work is mathematically represented through the area under the graph. The simplest case is when pressure is constant as shown in the graph below.

This reasoning can be extended in the processes with non-constant pressure as well. Thus, even if the pressure is changing, we can divide the curve over P - V diagram into small, constant pressure steps. The total area under the curve is therefore the sum of small rectangular areas. As we increase the number of rectangles by taking thinner rectangles, the error in calculation becomes smaller.

If we consider a certain rectangle (the i-th rectangle), the change in volume is ΔVi and the actual pressure is pi. Therefore, the work done to change the volume for this interval is

∆W_{i} = p_{i} × ∆V_{i}

Thus, the sum of all such intervals gives the total work. If we divide the graph in n squares, we can write for the total work:

W = ^{n}__∑___{i=1}p_{i} × ∆V_{i}

A gas sample expands from 3 L to 11 L against the standard atmospheric pressure. What is the work done by the gas during this expansion?

Since the pressure is constant, we can use the P∆V formula to find the work done by the gas.

To find the result in joules, we must use the units Pa and m^{3}. We know that the standard atmospheric pressure in pascals is P_{atm} = 100 000 Pa. Also, we have V_{1} = 3 L = 0.003 m^{3} and V_{2} = 11 L = 0.011 m^{3}. Therefore,

ΔV = V_{2} - V_{1}

= 0.011 m^{3} - 0.003 m^{3}

= 0.008 m^{3}

= 0.011 m

= 0.008 m

Now, we can apply the work formula for constant volume:

W_{by gas} = P_{gas} × ∆V

= 100 000 Pa × 0,008 m^{3}

= 800 J

= 100 000 Pa × 0,008 m

= 800 J

You have reached the end of Physics lesson **13.6.5 Finding Work using a P - V Diagram**. There are 6 lessons in this physics tutorial covering **The Kinetic Theory of Gases. Ideal Gases**, you can access all the lessons from this tutorial below.

Enjoy the "Finding Work using a P - V Diagram" physics lesson? People who liked the "The Kinetic Theory of Gases. Ideal Gases lesson found the following resources useful:

- P V Diagram Feedback. Helps other - Leave a rating for this p v diagram (see below)
- Thermodynamics Physics tutorial: The Kinetic Theory of Gases. Ideal Gases. Read the The Kinetic Theory of Gases. Ideal Gases physics tutorial and build your physics knowledge of Thermodynamics
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- Continuing learning thermodynamics - read our next physics tutorial: Pressure, Temperature and RMS Speed

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