Pressure, Volume & Temperature: Investigating the Relationship

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Discussion Overview

The discussion revolves around the relationship between pressure, volume, and temperature in the context of ideal gases. Participants explore the implications of changing pressure and volume while considering temperature changes, as well as the underlying principles governing these relationships.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that increasing pressure in a fixed volume vessel must lead to an increase in temperature, questioning if this relationship is fundamentally simple.
  • Another participant affirms the relationship between pressure and temperature, referencing Amontons' pressure-temperature law.
  • A different participant introduces the concept that rapid expansion of gas can lead to a decrease in temperature, citing its application in refrigeration and the Joule-Kelvin effect.
  • One participant reiterates the initial claim about pressure, volume, and temperature, emphasizing that increasing pressure in a fixed volume requires either an increase in temperature or the number of gas molecules, rather than temperature increasing to 'cancel' pressure.
  • Another participant agrees with the notion that pressure is uniquely determined by the state variables, and discusses the implications of changing these variables on the overall system.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the relationship between pressure and temperature, with some affirming a direct correlation while others challenge the simplicity of this relationship. The discussion remains unresolved regarding the nuances of how these variables interact under different conditions.

Contextual Notes

Participants reference the ideal gas law and its implications, but there are limitations in the assumptions made about the behavior of gases under varying conditions. The discussion does not resolve the complexities of these interactions.

Who May Find This Useful

This discussion may be of interest to those studying thermodynamics, gas laws, or anyone exploring the principles of ideal gases and their behaviors in various conditions.

fonz
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If the product of pressure and volume over temperature is equal to some constant for a particular ideal gas.

Let's say the volume is just a vessel and the pressure in the vessel is increased. So effectively the volume remains the same. Any increase in pressure must be canceled by an increase in temperature of the gas within the vessel is this correct? So by pressurising gas you are increasing the temperature?

Fundamentally is the relation between pressure and temperature this simple?

Thanks
 
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Yes, [itex]P \alpha T[/itex] and it's called Amontons pressure-temperature law.
 
Hi,
and the converse is interesting, the rapid expansion of a gas causes the temperature to decrease. This is used in refrigeration and and freezing sprays. A way of making carbon dioxide in schools often involves the rapid expansion of a CO2 fire extinguisher into a suitable chamber.
Look up the Joule-Kelvin effect.
Dave
 
fonz said:
If the product of pressure and volume over temperature is equal to some constant for a particular ideal gas.

Let's say the volume is just a vessel and the pressure in the vessel is increased. So effectively the volume remains the same. Any increase in pressure must be canceled by an increase in temperature of the gas within the vessel is this correct? So by pressurising gas you are increasing the temperature?
How are you increasing the pressure? You're keeping the volume the same, and if you pump more gas in then PV/T will increase. It's not that temperature increases to 'cancel' the increase in pressure; it's that you will have to raise the temperature to make the pressure go up.
 
I got to thinking,
It is true that pressure and volume over temp is a constant.
PV=NkT
I like the fact that this equation of state tells us the relationship between the state variables, pressure, volume and temperature. All of which are measurable quantities, (for an ideal gas).
So if we rearrange and think of what determines the pressure of your system.
P=(NkT)/V
So the only three ways to increase the pressure are to (V) decrease the volume, (T) increase the temperature and (N) increase the number of molecules. In your fixed vessel you have kept the volume constant, so you could only increase the pressure by either increasing the temperature or increase the number of molecules into the vessel. I agree with haruspex the temperature does not increase to cancel the pressure, it’s more like once you set the volume and the temperature for a fixed mass of gas the pressure is uniquely determined. Changing anyone of these variables will mean at least one of the other state variables must change to. Check out PVT surfaces, there ace.
Dave
 

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