Ideal gas law- Find the pressure

In summary, the conversation discusses a confusion about the pressure variable changing in a worked solution. The expert points out a typo and clarifies that the numbers are for volume, not pressure. The person realizes their mistake in algebra and corrects it.
  • #1
Woopa
21
4
Homework Statement
A container of an ideal gas that is isolated from its surroundings is divided into two parts. One part has double the volume of the other. The pressure in each part is p and the temperature is the same. The partition is removed. What is the pressure in the container now?
Relevant Equations
PV=nRT
Question:
1645529215001.png

Answer:
1645529385444.png

In the third last line of working, I do not understand why the pressure variable is changing? Shouldn't pressure remain constant and only the Volume change?
 
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  • #2
Woopa said:
In the third last line of working, I do not understand why the pressure variable is changing? Shouldn't pressure remain constant and only the Volume change?
Where do you see anything changing ? Strictly speaking ##p_{\rm\, final} ## is unknown and to be determined.
Then the outcome is ##p_{\rm \, final} = p##

Comment: they use capital ##P## in the solution, which is undesirable: once lower case ##p## , always lower case ##p##

##\ ##
 
  • #3
The 2 and 3 numbers are for V rather than for p.
 
  • #4
Lnewqban said:
The 2 and 3 numbers are for V rather than for p.
Do you mean it is a typo/ error in the worked solution?
 
  • #5
V + 2V = 3V
 
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  • #6
Lnewqban said:
V + 2V = 3V
Ah yes that make sense I can see now the numbers are actually for V, the way they've written out the equation has confused me.

However I am still arriving at the final answer P=2P. I must be making a mistake in my algebra. I will post my working in a moment
 
  • #7
1645540153027.jpg


Where is my mistake?
 
  • #8
##p⋅V/RT+p⋅(2V)/RT=p⋅(V+2V)/RT##
 
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  • #9
##pV+2pV=p(V+2V)=3pV##

You are saying that it's equal to ##6pV##. That's your error.
 
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FAQ: Ideal gas law- Find the pressure

1. What is the ideal gas law?

The ideal gas law is a mathematical relationship between the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is number of moles, R is the ideal gas constant, and T is temperature.

2. How do you find pressure using the ideal gas law?

To find pressure using the ideal gas law, you would rearrange the equation to solve for P. This would give you the equation P = (nRT)/V, where n is the number of moles, R is the ideal gas constant, T is temperature, and V is volume.

3. What units should be used for the variables in the ideal gas law?

The units used for the variables in the ideal gas law depend on the units used for the ideal gas constant, R. Typically, pressure is measured in atmospheres (atm), volume in liters (L), temperature in Kelvin (K), and number of moles in moles (mol). However, if a different unit of measurement is used for R, the units for the other variables may need to be adjusted accordingly.

4. Can the ideal gas law be used for all gases?

The ideal gas law is most accurate for gases at low pressures and high temperatures. At higher pressures and lower temperatures, the behavior of gases may deviate from the ideal gas law. Additionally, the ideal gas law assumes that there are no intermolecular forces between gas molecules, so it may not accurately predict the behavior of gases with strong intermolecular forces.

5. How is the ideal gas law used in real-world applications?

The ideal gas law is used in many real-world applications, such as in the design of engines and other machinery that use gases. It is also used in industries that deal with gases, such as the production of chemicals and the storage of compressed gases. Additionally, the ideal gas law is used in weather forecasting to predict changes in atmospheric pressure.

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