When does PV work come into play?

[supertrooper66]

When does PV work come into play versus PV=nRT? I know P is constant in PV work, so is that the answer? PV works come into play when pressure is constant? it's just sometimes it's not so obvious pressure is constant in the question, so then i'm lost

---

Members don't see this ad.

 

[Quantum Chem]

When pressure is constant you use w=p(delta V). If pressure is not constant you must integrate over that pressure change which turns out to be w= -nRTln(Vf/Vi). I don't think that'll be on the MCAT though.

 

[nfg05]

When does PV work come into play versus PV=nRT? I know P is constant in PV work, so is that the answer? PV works come into play when pressure is constant? it's just sometimes it's not so obvious pressure is constant in the question, so then i'm lost

"PV work" is most easily calculated when pressure is constant. As the previous poster noted, when P and V change throughout the course of a gas expansion integration is required (or area under a PV curve which could be a bit simpler if it's a geometric shape you're familiar with) which will not show up on an MCAT. Remember the four types of gas expansion (and compression):

Isothermal (constant temperature)
Adiabatic (no heat exchange)
Isovolumetric (constant volume, no work done by gas)
Isobaric (constant pressure)

Of these 4, isobaric is the one where you can easily calculate PV work with P(deltaV). If they don't tell you it's isobaric but they do give you a PV graph with a straight horizontal line representing an expansion, then clearly that expansion is isobaric and happening at constant pressure.

Both of these cases are pretty obvious, but I can't think of many situations where "it's not so obvious pressure is constant in the question" and you need to be focused on and/or able to quantify the PV work being done. Perhaps you could post a question you're confused on?

 

[physics junkie]

When pressure is constant you use w=p(delta V). If pressure is not constant you must integrate over that pressure change which turns out to be w= -nRTln(Vf/Vi). I don't think that'll be on the MCAT though.

OP, if you're interested he arrived at that result by rephrasing P in terms of V and integrating. so the integral of PdV equals the integral of (nRT/V)dV. That's where the log term comes in because the integral of dV/V = log(Vf)-log(Vi)

 

[supertrooper66]

okay, I realized why I was confused. when you said PV work does NOT have to be constant pressure, then it dawned on me.

i would post the question i'm confused on but it's on AAMC8 so i don't think i'm allowed to post it.

it was the tank question and asked what happens to pressure in gas of balloon when its volume is doubled.
using PV=nRT, I know the P would just halve since V is doubled. however, i thought it'd be better to use PV work. since thinking PV work HAD to be isobaric, i chose the answer that the pressure remains the same. however, with W=PV, as you said, P can change and P and V are inversely related there just as in PV=nRT. sooo, i guess i could technically use either equation to see the relationship between P and V? the balloon with a weight was ascending up the water tank, which i guess is an indication pressure is changing and is not constant? the answer was that P halved if you increased V by a factor of 2.

one thing i am still confused on is I thought n and T have to be held constant to say P=k/V, but T was changing in the question. i don't know, i guess i was just ovethinking it?

 

[physics junkie]

okay, I realized why I was confused. when you said PV work does NOT have to be constant pressure, then it dawned on me.

i would post the question i'm confused on but it's on AAMC8 so i don't think i'm allowed to post it.

it was the tank question and asked what happens to pressure in gas of balloon when its volume is doubled.
using PV=nRT, I know the P would just halve since V is doubled. however, i thought it'd be better to use PV work. since thinking PV work HAD to be isobaric, i chose the answer that the pressure remains the same. however, with W=PV, as you said, P can change and P and V are inversely related there just as in PV=nRT. sooo, i guess i could technically use either equation to see the relationship between P and V? the balloon with a weight was ascending up the water tank, which i guess is an indication pressure is changing and is not constant? the answer was that P halved if you increased V by a factor of 2.

one thing i am still confused on is I thought n and T have to be held constant to say P=k/V, but T was changing in the question. i don't know, i guess i was just ovethinking it?

The ideal gas law is an equation of state. PV and nRT both have units of energy. Essentially the ideal gas law is a statement about the conservation of energy in a gas. Because these factors(P, V, n, R, T) all go into calculating what the energy of a gas is we are able to make some statement about how they vary if you are dealing with a situation where energy is constant. If you don't add energy to the gas(temperature is solely a function of energy in an ideal gas) then T stays constant. So if T stays constant and you double the volume then the pressure has to be cut in half.

The P*dV equation is how to find the work done by a gas. Work = pressure*change_in_volume. Are you calculating work? No. Is work constant like nRT is constant? NO! Work is not a conserved quantity!

Work has units of energy so you might think it is a constant but kinetic energy has units of energy and it isn't a constant either. What is conserved then? TOTAL energy. If an object does work some of its potential or kinetic energy is changed into work. Total energy(kinetic + potential) is always conserved but kinetic or potential alone is not conserved. That's because kinetic energy can change into potential energy and vice versa.

http://en.wikipedia.org/wiki/Mechanical_work

http://www.lightandmatter.com/html_books/2cl/ch03/ch03.html#Section3.1
http://www.lightandmatter.com/html_books/2cl/ch03/ch03.html#Section3.5

It's difficult for me to explain fundamental concepts because I usually try to do so in terms of other concepts that I can't quite be sure you have a grasp of. If you want write out your thought process or any questions and I'll try to answer them.

 

[supertrooper66]

The ideal gas law is an equation of state. PV and nRT both have units of energy. Essentially the ideal gas law is a statement about the conservation of energy in a gas. Because these factors(P, V, n, R, T) all go into calculating what the energy of a gas is we are able to make some statement about how they vary if you are dealing with a situation where energy is constant. If you don't add energy to the gas(temperature is solely a function of energy in an ideal gas) then T stays constant. So if T stays constant and you double the volume then the pressure has to be cut in half.

The P*dV equation is how to find the work done by a gas. Work = pressure*change_in_volume. Are you calculating work? No. Is work constant like nRT is constant? NO! Work is not a conserved quantity!

Work has units of energy so you might think it is a constant but kinetic energy has units of energy and it isn't a constant either. What is conserved then? TOTAL energy. If an object does work some of its potential or kinetic energy is changed into work. Total energy(kinetic + potential) is always conserved but kinetic or potential alone is not conserved. That's because kinetic energy can change into potential energy and vice versa.

http://en.wikipedia.org/wiki/Mechanical_work

http://www.lightandmatter.com/html_books/2cl/ch03/ch03.html#Section3.1
http://www.lightandmatter.com/html_books/2cl/ch03/ch03.html#Section3.5

It's difficult for me to explain fundamental concepts because I usually try to do so in terms of other concepts that I can't quite be sure you have a grasp of. If you want write out your thought process or any questions and I'll try to answer them.

want to take my mcat for me?

i'm mainly confused on when work is done by gas then. i understand work done by gas is negative and work done on work is positive work. say i am squeezing a balloon, thus reducing its volume by a factor of 1/X. the pressure inside should increase by a factor of X, right? i don't know of a real life example when the work is being done BY the gas, though.

just to get this straight, is there NO net work done on or by an ideal gas then? i think there can be energy exchange between the system and its surroundings as long as equal energy is leaving as is entering, thus conservation of energy.