What's the deal with PV=nRT?

[Deanis]

Why does a decrease in volume result in an increase in temperature?

Conceptually, it makes sense - when you decrease volume, I assume you can't keep the pressure constant, and so pressure increaes, and having all those gas molecules close together seems like a good enough reason for temperature to rise. I'm not even sure if this reasoning is right, but even if it is, is still doesn't get around PV=nRT not working properly here.

Maybe the problem is that there is simply no way to keep pressure constant when decreasing the volume (when increasing the volume, we can keep pressure consttant by adding an inert gas)?

Any help here would be much appreciated.

Thanks.

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[UVAbme2009]

A constant pressure system is isobaric. Totally doable.

 

[TheGreatHunt]

This equation deals with an isolated gas. We're not talking about adding or subtracting gas from our sample here because that would change the variables in our equation. It honestly depends on what you are doing, you can isothermally compress a gas, and alternatively, you can isobarically compress a gas. You can have a gas do work, and you can have a gas do no work(let it expand into emptiness). Anyway, all these questions are answered in a course called "Thermodynamics" if you're really super interested, go check it out.

In order to answer your question though:

I think you're looking at this the wrong way. A decrease in Volume can be caused by a loss of temperature V= nRT/P, likewise, an increase in pressure can also be caused by a decrease in volume P = nRT/V (think of contracting a balloon). I think you're misinterpreting cause and effect here.

So to your question: "Why does a decrease in volume result in an increase in temperature?"

It doesn't. If you look at T=PV/nR or (V= nRT/P) then it is a LOSS of temperature that results in a loss of volume. It is also a GAIN of pressure that results in a loss of volume(Is caused by a loss of volume, whichever way you want to look at it). This may not seem intuitive at first, until you think of making a gas behave in a certain manner. Volume increase? Temperature must go up! Volume decrease? Temperature must go down! Think of a balloon that you warm up or cool down in warm water and an ice water bath.

Generally, it depends on if work is being done on the system, or what is happening, but again, this is thermodynamics... not the simple Ideal Gas Law.

 

[sleepy425]

i think you might be referring to adiabatic expansion of gases, which results in cooling. this property of adiabatic systems cannot be determined just by looking at PV=nRT because P, V, and T change.

This is why, if you have a cylinder of gas under very high pressure and you release the gas from the cylinder without a regulator, you'll start to see ice crystals forming at the opening, because the gas is cooling as it expands.

the derivation is a bit tricky, if you want to know it I can show you, but otherwise there's really no point.

I agree completely with thegreathunt though, that under isobaric conditions (constant pressure), when volume increases, so does temperature, because here P, n, and R are constants in PV=nRT, and so you just have V~T so when T increases, V increases.

Most reactions/systems are under isobaric conditions, because it's much easier to have a constant pressure system than to have a constant volume system. A constant pressure system is achieved by leaving the system open to atmospheric pressure, and so most chemical reactions are done under atmospheric pressure.

 

[Deanis]

Alright. Thanks guys.

I got confused because the EK book on Gen Chem ttalks about increasing the pressure which results in an increase in temperature (as mentioned by sleepy).

For the MCAT can I assume that we will always be dealing with the isobaric conditions?

 

[RPedigo]

Why does a decrease in volume result in an increase in temperature?

If pressure is constant (isobaric), then a decrease in volume results in a decrease in temperature. Your initial statement was incorrect, which was probably why you were confused.

Let's just assign everything to "1" (1 atmosphere, 1 liter, 1 mol, 1 K, and hell since R is a constant, let's just make that thing 1 also. This is just for conceptual thought.)
PV = nRT
(1)(1) = (1)(1)(1)
Both sides are equal to one.

Let's reduce the volume.

(1)(0.5) = (1)(1)(1)
Oh no! The left side is now 0.5 and the right side is still 1. This equation isn't right! So the system has to respond to fix it. If the number of moles is constant, the temperature must decrease to balance out the equation.

(1)(0.5) = (1)(1)(0.5)

So a decrease in volume causes a decrease in temperature, assuming pressure is constant.


Edit: saw it was already answered by TheGreatHunt above. Oops.

 

[RPedigo]

I got confused because the EK book on Gen Chem ttalks about increasing the pressure which results in an increase in temperature (as mentioned by sleepy).

The EK book is right in this regard as well.

Edit: Also moved your thread to the Q&A subforum for more discussion. Let me know if you have questions!

 

[physics junkie]

I didn't read any other posts in this thread. Just chiming in.
PV=nRT
nRT, or NkT, whichever you prefer, has units of joules. That is energy. Pressure*volume=energy. The equation is saying that if you take a gas with constant energy then an increase in volume equals a decrease in pressure. The equation relates 4 essential variables: P, V, n, and T. Depending on the situation you hold different variables fixed to get results from the equation.

For example, if you hold volume and moles of gas fixed and increase temperature then pressure must increase accordingly.

To extract useful information out of PV=NkT you need to hold two of the four variables constant. If you held only 1 variable as a constant and had 3 quantities varying such as P, V, and T at the same time then you could arrange countless numbers of ways the variables could interact.

The different types of commonly discussed processes: isobaric(constant pressure), isothermal(constant temperature), isochoric(constant volume) refer to situations where a variable is being held constant. N is generally assumed to be held constant because you usually have a fixed amount of gas if you're using PV=NkT.

 

[BerkReviewTeach]

Just adding my $0.02! It has been well addressed so far, but I want to chime in what I often see with many student's reasoning.

This is a perfect example where trust in equation supercedes common sense and can cause trouble. There is nothing wrong with using PV=nRT, but we need to consider the cause and effect.

If you heat a piston, it will expand. From an equation perspective, this is because Pext = Pint before and after, so P doesn't change and the piston is sealed, so n doesn't change. The conclusion and observation are that heating a gas within a sealed piston results in a net change in the volume that obeys Charles' Law of V1/T1 = V2/T2.

From a conceptual standpoint, heating the gas causes an increase in average kinetic energy which causes a temporary state where the collision force and frequency of the gas particles within the piston exceed those outside the piston, so it expands until the pressures equilibrate. The net impact is that V increased in response to T increasing. The equation and the concept are in alignment.

But, the reverse is not possible to observe in an isolated sense. If you pull the piston lid up, you decrease the internal pressure, raise the volume, and ulitmately cause a slight decrease in the temperature due to Carnot related issues (as molecules increase their average distance apart from one another, heat energy must be absorbed to overcome the intermolecular forces, which causes a drop in the heat energy resulting in a slightly reduced temperature). The cause and effect here are that raising the volume decreases P and decreases T, so while PV=nRT is obeyed, it does not help explain what is observed. Too much trust is being placed in equations without applying reasoning.

I see this also with V = IR. Blindly following the equation leads one to conclude that raising the resistance will cause the voltage of a battery to increase. While the equation supports the notion, it is physically unintuitive. The battery and the resistor are independent devices. The cause and effect here is that raising the resistance will reduce the current, but the voltage of the circuit depends solely on the battery's emf (assuming no voltage drop internally due to a temperature change over time).

The moral to the story is that you need to apply physical intuition on the MCAT more than you need to blindly follow equations. At least that's the way I/we try to teach it.

$0.02 inserted, so I will fade away now.

 

[Deanis]

Thanks a lot everyone! Much obliged.

And while we're on the topic...

Under high pressure and low temperature:

TPR says V(real) < V(ideal)

whereas

EK says V(real) > V(ideal)

I think TPR might be referring to effective volume (the volume not occupied by the molecules themselves), but I'm not sure. Which one should I take to be truth on the MCAT? EK seems to be more intuitive.

 

[physics junkie]

Thanks a lot everyone! Much obliged.

And while we're on the topic...

Under high pressure and low temperature:

TPR says V(real) < V(ideal)

whereas

EK says V(real) > V(ideal)

I think TPR might be referring to effective volume (the volume not occupied by the molecules themselves), but I'm not sure. Which one should I take to be truth on the MCAT? EK seems to be more intuitive.

The V in PV=nRT refers to the volume of the container not occupied by the gas. For an ideal gas one of the assumptions is that the particles have no volume. When you deal with an extreme environment you use the van der waals equation for a real gas (P+a(n/v)^2)(V-nb) = nRT you see that the volume is less than with the ideal gas law by a factor nb. n is the number of particles, b is a constant referring to the volume of a single particle. If you want a breakdown of what the van der waals equation means I explained it in depth in another thread--just search my user name's posts. Oh, and ignore the guy who disagreed with me, he didn't know what he was talking about.

EK is saying the volume of the gas is greater--which is obvious because ideal gas particles have no volume.

 

[bluemonkey]

The V in PV=nRT refers to the volume of the container not occupied by the gas. For an ideal gas one of the assumptions is that the particles have no volume. When you deal with an extreme environment you use the van der waals equation for a real gas (P+a(n/v)^2)(V-nb) = nRT you see that the volume is less than with the ideal gas law by a factor nb. n is the number of particles, b is a constant referring to the volume of a single particle. If you want a breakdown of what the van der waals equation means I explained it in depth in another thread--just search my user name's posts. Oh, and ignore the guy who disagreed with me, he didn't know what he was talking about.

EK is saying the volume of the gas is greater--which is obvious because ideal gas particles have no volume.

Dude...What is your problem? Do you really want to dig up that old thread???

 

[physics junkie]

Dude...What is your problem? Do you really want to dig up that old thread???

I don't know who you are so I'm not quite sure why you're so offended by my comments(in this thread or that one). I said to ignore your posts because I found a lot of errors in them in addition to truths that make a tough equation even tougher to understand(The equation is tough, not the concepts). I recommended he look at the thread because after you stopped posting in it I posted a very long detailed explanation of the van der waals equation that another user found helpful(or at least so he says in that thread). I dealt very specifically with the issue of what "P-real" and "V-real" are in that post which is the same thing as what this guy is asking about. That thread does read like a mess but if he ignores the parts where you and I interact or where you responded he would be better off. Everything I said in that thread was correct. I don't know why you think I shouldn't recommend he read it just because you "disagreed" with me in it. I use quotes because you never took the time to reply point by point to my criticisms and instead renumerated the parts of your post that I didn't dissect.

In response to whether or not I'm interested in digging up that old thread if you want to go back and reply to my criticisms and discuss the VDW equation maturely then yes, I am willing to dig it up. I post here because I enjoy physics and by explaining it to others I learn it better myself. If you find any errors in my posts in that thread then feel free to post them in that thread and I'll respond only to the physics.

If you have a personal problem with me then you can discuss it with me in a private message if you really want. Let's not pollute this thread.

 

[BerkReviewTeach]

{{{physics junkie and blue monkey}}}

You both post some brilliant, highly-beneficial comments in this Q&A section. Your comments make up a large amount of information that really help make this site better.

It would suck significantly if we lost either of you to something as trivial as an argument in a thread. We all have a certain arogance anytime we decide to post an answer to a question, so it's bound to step on someone's toes at some juncture. It comes with the territory.

I just deeply hope that you guys (no gender implied by the term) can just say F-it and move on.