Work, heat and internal energy in pV diagram.

[Gavroy]

hi

i have this pV-diagram(ideal gas) and i am supposed to say something about the heat, internal energy and work transferred and done on these different paths( i have to bring them in an order like). i do not know how to do this, as this is a pV diagram and these paths are not further specified. i guess that i only need two quantities, as the third quantity is related to the other two by the 1st law of thermodynamics.

 

[mfb]

I would begin with work: It is done when the volume changes. Can you relate volume changes to "work per volume", if you know the pressure?

Heat changes the pressure at constant volume. Try to begin with path 1, and look what happens there.

A qualitative description should be sufficient, as you just have this sketch to describe the paths.

 

[Gavroy]

in my opinion the resulting change in volume and pressure is the same, so i do not see how this is helpful, sorry.

 

[mfb]

The values for pressure and volume are the same at the end, but the paths are different.

Imagine you are in a car: You have a lot of different ways to reach any destination. Some of them are quicker than others, some of them require more fuel, and so on. So if I ask you "which way is the quickest?", the answer "they all lead to the same destination" is not useful.

Here is my question: Which path releases the lowest amount of work?

 

[Studiot]

Follow mfb, he is leading you down the correct path

heat, internal energy and work transferred and done on these different paths

Further hint
Which of these does not appear in a PV diagram?

 

[Gavroy]

releases the lowest amount? probably the shortest one.

so 2-3-1-4?

what does not appear? probaby, heat, but i don't know. one could say, that internal energy depends only on temperature and there is the ideal gas law, so one could say something about the internal energy too.

 

[Studiot]

What quantity is measured by the area under a PV diagram and what quantities are defined by the end points in your diagram?

 

[Gavroy]

work is the area under this curve.
internal energy is defined by the end points.

 

[Studiot]

OK keep going you are getting there.

See you in a couple of hours.

 

[256bits]

You might start with an idealized PV diagram such as that to to say something about the heat, internal energy and work transferred and done on these different paths. And then compare the paths in your question to the idealized.

 

[Gavroy]

but was it not correct that the amount of work is proportional to the area under the curve and the internal energy is the same? cause then, i would say: problem solved.

 

[mfb]

Heat is still missing.
But apart from that... yes.

 

[Studiot]

I don't know what sort of course you are following but this is really first law/gas law stuff and you have already asked questions involving the second law.

Anyway your question here is to think about PV diagrams so here are some notes on PV diagrams.

Note that isothermal and adiabatic expansions are concave upwards.

At the end are two cases from your diagram. A straight line from P₁V₁ to P₂V₂ and a line which goes upwards from P₁V₁ so meaning that the process increases both P and V. That is they are concave downwards.

What do you think these imply?