Boyles Law Graphs: PV vs Pressure Explained

  • Thread starter TheRedDevil18
  • Start date
  • Tags
    Graphs Law
In summary: Together, these two equations state that k = R*T. So k is proportional to temperature, though not exactly equal to temperature.
  • #1
TheRedDevil18
408
1
Hi, what would be the relationship between the product of pressure and volume (pv), against pressure. How would you represent it on a graph?, I have heard that the shape will be a horizontal line. Could someone please show an example or explain it to me?
 
Chemistry news on Phys.org
  • #2
See, for example, this website at NASA. You should feel free to plot the product of pressure and volume against pressure given their demonstration for yourself. You could also plot the product against volume for completeness's sake.
 
  • #3
Thanks, with the graph volume vs 1/pressure, I should just take the pressure and invert it and then sketch the graph eg. pressure 150kpa = 1/150 = 0.007. Is their any other calculations?
 
  • #4
TheRedDevil18 said:
Hi, what would be the relationship between the product of pressure and volume (pv), against pressure. How would you represent it on a graph?, I have heard that the shape will be a horizontal line. Could someone please show an example or explain it to me?

The product PV for an ideal gas is constant, assuming no excess moles were added. So if you plot it against the pressure or the volume, it gives you a horizontal straight line.

Thanks, with the graph volume vs 1/pressure, I should just take the pressure and invert it and then sketch the graph eg. pressure 150kpa = 1/150 = 0.007. Is their any other calculations?

Yes, just calculate the corresponding 1/P for V. The graph is of the equation,

[tex]V = \frac{k}{P}[/tex]

[tex]PV = k[/tex]

From mathematics, this comes out to be a rectangular hyperbola.
 
Last edited:
  • #5
So in my example pressure = 150 kPa and Constant = 1530, it will become 1530/150 = 10.2 which is my volume, so its like plotting volume against volume, so my graph is a straight line?, Are you sure this is correct? and also what does the gradient represent, is it temperature?
 
Last edited:
  • #6
TheRedDevil18 said:
So in my example pressure = 150 kPa and Constant = 1530, it will become 1530/150 = 10.2 which is my volume, so its like plotting volume against volume, so my graph is a straight line?, Are you sure this is correct? and also what does the gradient represent, is it temperature?

Whoops. You do calculate the 1/P, for V and plot the graph. I misinterpreted your previous post and told you the hyperbolic relation for P and V, and not 1/P and V..

The graph between 1/P and V would simply be a straight line, as it is of the form y=mx ( or V=k/P). This line passes through the origin and has the slope k.
 
Last edited:
  • #7
So to get 1/P, it would be V=k/P, right?, and does the gradient represent temperature?
 
  • #8
TheRedDevil18 said:
So to get 1/P, it would be V=k/P, right?, and does the gradient represent temperature?

Yep. The gradient does not represent temperature, though. Since gas is ideal and assuming one mol,

[tex]k = PV = RT[/tex]

So, k is proportional to temperature, though not exactly equal to temperature.
 
  • #9
So k = RT, what does RT represent?
 
  • #10
TheRedDevil18 said:
So k = RT, what does RT represent?

Do you know the Ideal gas equation?

R is the universal gas constant, and T is temperature of the gas.
 

1. What is Boyle's Law and how does it relate to PV vs Pressure graphs?

Boyle's Law states that, at a constant temperature, the pressure of a gas is inversely proportional to its volume. In other words, as pressure increases, volume decreases and vice versa. This relationship is visualized on a PV vs Pressure graph, where pressure is plotted on the y-axis and volume is plotted on the x-axis.

2. What is the ideal gas law and how does it differ from Boyle's Law?

The ideal gas law is a combination of Boyle's Law, Charles's Law, and Avogadro's Law. It states that the product of pressure and volume is directly proportional to the temperature and the number of moles of gas present. This law takes into account the effects of temperature and amount of gas, whereas Boyle's Law only considers the relationship between pressure and volume at a constant temperature.

3. What does a straight line on a PV vs Pressure graph represent?

A straight line on a PV vs Pressure graph represents a constant temperature. This is because Boyle's Law only holds true at a constant temperature, so a straight line indicates that the temperature is being held constant while pressure and volume are changing.

4. How can Boyle's Law be used to predict the behavior of gases?

By using Boyle's Law, scientists can predict how a gas will behave under different pressures and volumes. For example, if the pressure of a gas is increased while the volume is kept constant, the temperature will also increase. This can be useful in various industrial and scientific applications such as in the design of gas storage tanks and the compression of gases for use in engines.

5. Are there any limitations to Boyle's Law and PV vs Pressure graphs?

Yes, there are a few limitations to Boyle's Law and PV vs Pressure graphs. First, it only applies to ideal gases, which do not exist in real life. In real gases, there are intermolecular forces that can affect the relationship between pressure and volume. Additionally, Boyle's Law only holds true at a constant temperature, so any changes in temperature can affect the accuracy of the predictions. Finally, the law assumes that all other variables, such as amount of gas, remain constant. In real-life situations, this may not always be the case.

Similar threads

Replies
14
Views
1K
Replies
2
Views
504
  • Advanced Physics Homework Help
Replies
11
Views
1K
Replies
3
Views
841
Replies
0
Views
489
Replies
4
Views
3K
Replies
10
Views
2K
Replies
7
Views
23K
Replies
3
Views
2K
Back
Top