B Laws in Otto, Diesel, etc. cycles

1. May 13, 2018

physea

Hello guys,

I am a bit confused. Is it that PV/T=constant for ALL the processes of ALL cycles, like Otto, Diesel, Rankine?
I know that PV=mRT, so does that mean that PV/T=constant all the time?

Secondly, I am a bit confused as I read that PV^γ=constant. What is that exactly? Where does it come from and when does it apply?

Thanks!

2. May 13, 2018

olgerm

It is constant in ideal gas if number of moleculs remains constant.

3. May 13, 2018

physea

I know that, I think it was clear when I wrote PV=nRT? (or mRT)

But what is PV^γ=constant, where it comes from, where it applies?

Also, where is the temperature highest in the Otto cycle? I would assume it is where PV is highest, but how can one know?

4. May 13, 2018

Staff: Mentor

No, not all the time. Explosions and shock waves don't follow the perfect gas law.

Where does it come from? Statistical Mechanics https://en.wikipedia.org/wiki/Statistical_mechanics

The key word is equilibrium. Explosions and shock waves are non-equilibrium for brief intervals of time.

5. May 13, 2018

Mister T

No, it wasn't. This question makes that clear.

The ideal gas law is an approximation. Approximations are approximately valid under some circumstances, but there are circumstances where they are very far from valid.

6. May 13, 2018

physea

OK, I am talking about UNDERGRADUATE PHYSICS, or if you prefer HIGH SCHOOL physics and as I cleared in the begining, Otto, Diesel, Rankine IDEAL cycles.

So PV^γ=constant only in adiabatic processes and this is an ADDITIONAL formula to the PV=constant? So in adiabatic processes both PV and PV^γ are constant?

Also, does anyone know the difference between η(Otto) and η(thermal) as below ?

I don't know what are the definitions of these two efficiencies, I don't know why there are even two efficiencies, it doesn't make sense.

7. May 13, 2018

Staff: Mentor

OK, I'll change the prefix on this thread to B if that's more appropriate.

Edit: All your questions can be answered in the Wikipedia article. https://en.wikipedia.org/wiki/Perfect_Gas_Law
Please study that. If there are parts of that you don't understand, then post again.

8. May 13, 2018

Mister T

So was I.

No, $PV=nRT$ would be the additional formula.

No. $PV$ is constant for an isothermal process. $PV^\gamma$ is constant for an adiabatic process.

Where did you find these two expressions for the efficiency?

In an engine cycle what does the area enclosed within the loop on the $PV$ diagram tell you?

What is the general definition of the efficiency of any engine?

9. May 13, 2018

physea

I found them in the notes handed to me, they should be equal each other I suppose?
Definition is the net work over heat supplied with net work being q supplied minus q exiting.

Last edited: May 13, 2018
10. May 17, 2018

physea

Guys,

In ideal Rankine cycle, we say that during the isobaric expansion, Qin = Δh. However, isn't the correct Qin - W = Δh -> Qin - PΔV = Δh?

Last edited: May 17, 2018
11. May 17, 2018

physea

Something else guys, let's say you know all the P,V,T of a 4 stroke Otto engine. You also know the rpm and the compression ratio.

Are you able to find the power of the engine? I think from Cv and T, you find the Qin and the Qout, thus the Wnet.

But that would be in kJ/kg, so don't you need the mass flow rate to be able to calculate power?

12. May 18, 2018

physea

Anyone?

13. May 18, 2018