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AP Physics 2: Exam Prep27 chapters | 158 lessons | 13 flashcard sets

Instructor:
*Laura Foist*

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

Pressure and volume are measured in order to determine work done in some systems. In this lesson we will learn how to plot pressure and volume and what we can calculate from the plot.

The car you drive to school is probably a gasoline engine. Gasoline engines use pistons, which use changing pressure and volume in order to get work done.

To see what is happening in a system, such as the pistons in a car, we can graph pressure vs volume, with pressure on the y-axis and volume on the x-axis. Let's look at a few different data sets. First let's see constant volume:

When we graph this we see we get a straight vertical line:

Now let's look at one with constant pressure:

When we graph this, we see we get a straight horizontal line:

Finally, let's look at one with constant temperature:

When we graph this, we see we get a hyperbola:

These are the different general shapes we can see in a pressure vs. volume graph.

Now, let's look at the ideal gas law, where pressure times volume equals *n* number of moles multiplied by the universal gas constant (R) times temperature:

PV = nRT

If we are in a closed system where we aren't losing any gas particles, then *n* is constant, and R is always constant, so we know that PV is proportional to T. In other words as either pressure or volume is doubled, temperature is also doubled.

If both pressure and volume are doubled, then temperature is quadrupled. If pressure is doubled and volume is cut in half, then there is no change in temperature.

Now, we know that temperature is directly proportional to internal energy (U), so this means that U is also directly proportional to PV.

So, let's look at plot 1 and determine the changes in internal energy:

From beginning to end the pressure is cut in half, and there are no changes in volume, so the internal energy is also cut in half. Now let's look at plot 2 and determine the changes in internal energy:

From beginning to end the pressure had no changes, and the volume is doubled, so the internal energy is also doubled. Now let's look at plot 3 and determine the changes in internal energy:

From beginning to end the pressure is cut in half and the temperature was doubled, which means that there were no overall changes on the internal energy, which makes sense since this is the plot for no changes in temperature.

In order to calculate work from the plot, we simply need to calculate the area under the curve. For plot 1, with constant volume, this is fairly simple:

There is no area under the curve, because the change in volume is equal to 0. So no work was done. Now, let's look at plot 2:

We went over 8 and up 5, so the area of the rectangle under the curve is equal to 8 x 5 = 40.

For plot 3, we would need to use integrals to determine the area under the curve. Using the actual integral we find that the work done is equal to 519 J.

According to the first law of thermodynamics the change in internal energy is equal to heat plus work. This means that we can determine heat by taking the change in internal energy and subtracting work.

So, for plot 1, the change in internal energy was 0.5 and the work done equals 0. So the heat is equal to 0.5 - 0 = 0.5.

For plot 2, then change in internal energy was 2, and the work done was 40. So, the heat is equal to 2 - 40 = -38

For plot 3, the change in internal energy was 0 and the work done was 519. So, the heat is equal to 0 - 519 = -519

Pressure and volume change in pistons, which is what drives the work to occur in order for gasoline engines, and other products, to run. We can graph pressure vs volume, with pressure on the y-axis and volume on the x-axis. From this plot we can determine:

- change in internal energy as a direct relationship to the change in volume in pressure.
- work by calculating the area under the curve on the plot.
- heat produced in the system by subtracting work from internal energy.

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AP Physics 2: Exam Prep27 chapters | 158 lessons | 13 flashcard sets

- Internal Energy of a System: Definition & Measurement 4:20
- Calculating Changes in Kinetic & Potential Energy of a System
- Work: Definition, Characteristics, and Examples 4:38
- Power: Definition and Mathematics 5:24
- Work-Energy Theorem: Definition and Application 4:29
- Work Done by a Variable Force 7:10
- Pressure-Volume Diagram: Definition & Example
- Mechanisms of Heat Transfer: Conduction, Convection & Radiation 9:19
- First Law of Thermodynamics: Law of Conservation of Energy 7:42
- Changes in Heat and Energy Diagrams 8:09
- Plotting Pressure vs. Volume for a Thermodynamic Process
- Applying Conservation of Mass & Energy to a Natural Phenomenon
- Go to AP Physics 2: Conservation Principles

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