Reflections on Pressure vs. Volume

In our pressure vs. volume investigation, we've examined three different models. Model I is a liner, model II is proportional, and model II is inversely proportional.  

In model I, liner, the graph's declining line seemed to be off of the data points in the unadjusted volume plot. The case has remained the same for adjusted, +0.8mL extra volume in the measuring apparatus, the pressure syringe. The linear model has failed to go through any of the collected data points. The RMSE is the same for both the original and adjusted volume at 24kPa.

In model I, we used the equation y=mx+B, where the value of y would increase/decrease depending on the value of the slope (m) and the value of x. 

In model II, proportional, the line's curve has a better chance of going through, or nearby, the collected data points.  For the unadjusted volume graph, the line's curve went through 50% of the points (total four points) and passed nearby the other two points. When the same model is applied to the adjusted volume of +0.8mL, the line's curve touched 100% of the points. The RMSE is changed dramatically from 7.1kPa for the unadjusted volumed to 1.7kPa in the adjusted volume graph.

For this model, we used the equation y=Ax, where the relationship between x and y is proportional. Thus any addition to the x values will proportionally affect the outcome of the y values. 

In model III, inversely proportional, where the graph is pressure vs. the inverse of the volume (mL⁻1), the graph's positive line has touched 25% of the collected points, while it went through 100% of the points for the inverse volume plot. The inverse proportional graph demonstrated the proportional relationship between pressure and the inverse function of volume, which is another way of saying the inverse relationship between the pressure and volume. The RMSE difference between the inverse adjusted and the inverse unadjusted volume is high. We have 6.13kPa for the unadjusted inverse volume, while the adjusted inverse volume showed a 1.54kPa in value.

In this model, we used y∝1/x or y=A/x, where A is the proportionality constant. 

The constant of proportionality is the ratio in any proportional relationship. It can be shown as A=y/x or y=Ax

What that means if we had a table of the following values:

x        y

1        2

2       4

3       6

We can easily infer that the constant of proportionality here is two because the y value is the product of A(x).

For the inverse-proportional relationship, the slope of the line is:

On the average, the pressure increase by 1.11E03 for every mL⁻1

The value of 0mL⁻1 would be on the right side of the pressure vs. inverse volume graph. As we approach 0mL⁻1 in volume, the value of pressure will start to reach infinity. Therefore, I don't think that there is a physical meaning to that point.