Laws in Otto, Diesel, etc. cycles

[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!

 

[olgerm]

Is it that PV/T=constant for ALL the processes

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

 

[physea]

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

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?

 

[anorlunda]

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

A sufficient (but not necessary) condition for statistical equilibrium with an isolated system is that the probability distribution is a function only of conserved properties (total energy, total particle numbers, etc.).[1] There are many different equilibrium ensembles that can be considered, and only some of them correspond to thermodynamics.[1]Additional postulates are necessary to motivate why the ensemble for a given system should have one form or another.

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

 

[Herman Trivilino]

I know that, I think it was clear when I wrote PV=nRT?

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

does that mean that PV/T=constant all the time?

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.

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

Do a google search for adiabatic process.

 

[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.

 

[anorlunda]

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.

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.

 

[Herman Trivilino]

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 was I.

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

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

So in adiabatic processes both PV and PV^γ are constant?

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

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.

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?

 

[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.

 

[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?

 

[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?

 

[physea]

Anyone?

 

[Chestermiller]

Anyone?

Can you please ask each of your questions in separate threads? We feel like we're trying to hit a moving target.