Laws in Otto, Diesel, etc. cycles

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Discussion Overview

The discussion revolves around the thermodynamic principles governing various engine cycles, specifically the Otto, Diesel, and Rankine cycles. Participants explore concepts such as the ideal gas law, the relationship between pressure, volume, and temperature, and the conditions under which certain equations apply, particularly in adiabatic processes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • Some participants question whether the relationship PV/T=constant applies to all processes in all cycles, noting that it holds for ideal gases under certain conditions.
  • There is confusion regarding the equation PV^γ=constant, with participants seeking clarification on its derivation and applicability, particularly in adiabatic processes.
  • One participant asserts that explosions and shock waves do not follow the ideal gas law, indicating limitations of the law in non-equilibrium situations.
  • Participants discuss the distinction between isothermal and adiabatic processes, with some asserting that PV is constant in isothermal processes while PV^γ is constant in adiabatic processes.
  • There is a query about the definitions and differences between two types of efficiency (η(Otto) and η(thermal)), with participants expressing confusion over why two efficiencies exist.
  • One participant raises a question about the calculation of power in an ideal Rankine cycle, suggesting that knowledge of P, V, T, and other parameters is necessary for determining power output.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the ideal gas law and the conditions under which various equations hold. There is no consensus on the definitions of efficiencies or the calculations related to the Rankine cycle, indicating ongoing debate and uncertainty.

Contextual Notes

Limitations include the dependence on ideal gas assumptions, the need for clarity on definitions of efficiency, and unresolved questions regarding the calculation of power in engine cycles.

physea
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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!
 
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physea said:
Is it that PV/T=constant for ALL the processes
It is constant in ideal gas if number of moleculs remains constant.
 
olgerm said:
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?
 
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.
 
physea said:
I know that, I think it was clear when I wrote PV=nRT?

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

physea said:
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.
 
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 ?

upload_2018-5-13_16-34-17.png


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.
 

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physea said:
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.
 
physea said:
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?
 
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.
 
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  • #10
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?
 
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  • #11
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
Anyone?
 
  • #13
physea said:
Anyone?
Can you please ask each of your questions in separate threads? We feel like we're trying to hit a moving target.
 

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