# PdV or Vdp

1. Jul 26, 2011

### dries

If you have to calculate the ammount of energy needed to perform a compression of the ammount of energy is gained by expanding. Then I don't know when to use the integral
W = int pdV
and when
W = int Vdp

2. Jul 26, 2011

### Studiot

If you compress something does the volume change?

3. Jul 26, 2011

### dries

the process is isentropical (so yes)

4. Jul 26, 2011

### Studiot

If the volume changes why are you contemplating Vdp?

5. Jul 26, 2011

### dries

using the isentropic equation
pV^k = constant = p1V1^k
you can write V in function of p so you get another integral

int (p1/p)^(1/k)*V1 dp
=
p1^(1/k)*V1 * int p^(-1/k) dp

An analog conversion is possible for the pdV, but i found both as methode to calculate the required energy. Now I wan't to know when i have to use which one

(thanks for the fast responses allready)

6. Jul 26, 2011

### Studiot

PdV states the volume change at constant pressure.

So you use this for thermodynamic processes carried out at constant pressure eg the free expansion of a gas against the atmosphere, most chemical reactions, carried out in an open beaker.

VdP states the change in pressure at constant volume so you would use this when say inflating a bicycle tyre or gas cylinder, whose volume does not change.

7. Jul 26, 2011

### dries

P or V don't have to be constants as shown in previous formule of isentropic change, they can be dependent of eachother. Imagine a compressor, both volume and pressure changes when the air is being compressed.

8. Jul 26, 2011

### Studiot

Are you telling me or asking me?

9. Jul 26, 2011

### jack action

PdV is the reversible work done on a system by changing the volume.

VdP is the change in enthalpy for a process which is both reversible and adiabatic (or isentropic).

So, if your process occurs in a http://en.wikipedia.org/wiki/Thermodynamic_system#Closed_system" (where there is no mass flow in or out), you use PdV.

If the process occurs in an http://en.wikipedia.org/wiki/Thermodynamic_system#Open_system" (where there is mass flow coming in or out), you use vdP.

Last edited by a moderator: Apr 26, 2017
10. Jul 27, 2011

### dries

Thanks a loth for the valuable reply!

11. Jul 27, 2011

### Studiot

Good morning, jack action

Can we apply them to a real calculation, say the work done by the gas in expanding

100 litres of neon at 0o C and 10 bar (atmosphere) of pressure, expanded to 1 bar (atmosphere) of pressure

1) Via a reversible isothermal process

2) via a reversible adiabatic process

3) via a sudden (nonreversible) adiabatic process

Are the above systems open or closed?

I make the answers

1) 232 850 Joules

2) 91410 Joules

3) 54740 Joules

12. Jul 27, 2011

### jack action

I think I'm right, but I'm open to discussion. My experience is based on engine processes.

For example, when you compress the air inside the cylinder with the valve closed, that is a closed system. In this case, the work input needed by the piston will be PdV (which is CvdT for an isentropic process as shown in my previous link).

But if you achieve the same compression with a turbine which has open ends with continuous airflow, that is an open system. In this case, the work input needed by the turbine will be VdP (which is CpdT for an isentropic process as shown in my previous link). In this case, you also need to take http://en.wikipedia.org/wiki/Stagnation_temperature" [Broken] into account, since the fluid is in motion at the inlet and outlet.

Work required by an open system is then larger than work required by a closed system since Cp > Cv.

The OP did say the process was isentropic but was not more specific. You're talking about an isothermal process, which I would treat as an isentropic process with heat addition (or removal), which is described in my previous links for both closed and open systems.

As for determining if the free expansion of a gas against the atmosphere is an open or closed system, I haven't really thought of it, but I would risk an answer by saying it is a closed system. The system would be the entire atmosphere where no fluid comes in or out.

Last edited by a moderator: May 5, 2017
13. Jul 27, 2011

### Studiot

Hello, jack, the OP was not very clear but seemed to want to know when to use PdV and when to use VdP in calculating the work term in thermodynamic processes.

This was particularly muddled

I was trying to lead him towards a sensible understanding and statement before he seemed to start arguing the toss.

However the question, as I have posed it, is a reasonable one that troubles many and deserves an airing.

Actually I was talking about three different types of process (for good reasons) and put my results where my mouth is.
I will happily display the calculations ( they each only a few lines long) and discuss those reasons, but I wondered if you got the same values?

One of the keys to getting thermodynamic calculations right is to correctly define the system boundaries.

Another is clearly to use the correct equations.

You are talking about the flow version of the first law or if you like a modified Bernoulli in you turbine.