What is Polytropic: Definition and 52 Discussions

A polytropic process is a thermodynamic process that obeys the relation:




p

V


n


=
C


{\displaystyle pV^{\,n}=C}
where p is the pressure, V is volume, n is the polytropic index, and C is a constant. The polytropic process equation can describe multiple expansion and compression processes which include heat transfer.

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  1. M

    Solving Unusual Problems: Using the Polytropic Ideal Gas Equation

    My teacher likes to make really weird problems. How can I start this problem? The only thing I thought of doing is using the polytropic ideal gas equation when cp= constant. (p2/p1)^k-1/k = T2/T1 and making p1 and t1 in each case the normal state of the lungs
  2. M

    When to use the adiabatic index in the polytropic process formulae?

    Hi, I was doing this question and I was slightly confused as to whether I ought to just substitute n = \gamma (the adiabatic constant) into the equation? The answers don't do this, but I was wondering why it was wrong for me to do so? This was only a small fraction of the question (which was...
  3. N

    Polytropic Process equation [Thermodynamics]

    Hello there, So yesterday my thermodynamics professor did some black magic and transformed our beloved equation (1/(1-n))*(p1v1-p2v2) into (n/(n-1))*(p1v1-p2v2), but i didnt understand why he did it and how (he is too fast for my writing). Does anyone know how he did it, are there any...
  4. C

    What is the intuitive meaning behind the polytropic process.

    What does it actually mean from an intuitive standpoint? I don’t want to simply memorize the equation. What is it really and when can it be used? What is the usefulness of it? Thanks.
  5. J

    What are the steps to solve a polytropic process problem?

    Homework Statement At the start of a compression, a cylinder contains 0.04 m^2 of some ideal gas at a pressure of 100kPa and a temperature of 110 degrees. Compression takes place according to the law: P(V)^1.27 = constant The gas undergoes a two stage process: compression from 0.04 m^3 to...
  6. F

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  7. HethensEnd25

    How to Derive PdV=RdT/(1-δ) from the Polytropic Process Constant Equation?

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  8. gsyz

    How can heat capacity be determined when both pressure and volume are changing?

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  9. V

    I Where does a polytropic EoS come from?

    I have read few texts about compact objects (neutron stars, white dwarfs) and the easiest approximation of equation of state is taken as a polytrope. But nowhere is written why, how can I derive it or from what (or I missed it). Can someone explain me it or refer me to some text? Thank you.
  10. R

    B Polytropic process with heat addition

    In polytropic process if we know p1,v1,v2 and q(heat added in process) then what will be the value of p2 and the coff. Of expansion (n) ?
  11. S

    Help to understand polytropic exponent and efficiency

    Hello all, I am new to thermodynamics applied to turbines and compressors and I am trying to get my head around what is represented when calculating the work of a compression/expansion process using the polytropic exponent as oppose to the specific heat ratio of 1.4 (I'm working with air). The...
  12. J

    How Do You Calculate the Polytropic Process Index 'n' in Thermodynamics?

    Homework Statement "Determine the polytropic process index 'n' from the initial and final condition parameters of the air (gas) in the air compressor cylinder." Im struggling with this question on my thermodynamics coursework and was wondering if anyone could help me out a little bit...
  13. R

    Ideal Gas Equation and Polytropic Constant

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  14. jdawg

    Conceptual polytropic question

    Homework Statement Can someone give me an explanation of a polytropic process and maybe an example? I know it obeys pvn=constant, but I can't seem to find a definition that makes this concept click in my head. Would you consider isobaric, isothermal, and isochoric processes to be polytropic...
  15. JasonHathaway

    Thermodynamics: Polytropic Process

    Homework Statement Q1- 0.15 kg of air (Ideal) compressed in a polytropic process (PV1.5=C) from 0.06 m3 to 0.01 m3. If the initial pressure was 0.25 MPa. Determine: 1- The initial temperature and the final pressure. 2- The work done during the process. Homework Equations P1 V1 = m R T P1...
  16. Z

    Polytropic Process of Nitrogen

    Homework Statement Nitrogen at 100°C and 600 kPa expands in such a way it can be approximated by a polytropic process with n=1.2. Calculate the work and the heat transfer if the final pressure is 100 kPa. Homework EquationsThe Attempt at a Solution I used the equation T2/T1=(P2/P1)^[(n-1)/n]...
  17. Mingsliced

    Thermodynamics - Work Done in a Closed System (Polytropic?)

    Just want to check that I've used the correct method for this thermodynamics question I've been set. Any clarification would be greatly appreciated. So I have a closed system in which a gas is compressed from a pressure of 3 bar absolute to 5 bar absolute. The volume changes from 0.9m^3 to...
  18. mef51

    [Thermodynamics] Heat Capacity for Polytropic Process

    Consider an ideal gas. For a polytropic process we have ##PV^n = const##. Different values of ##n## will represent different processes; for example isobaric (##n=0##), isothermal (##n=1##), and isochoric (##n=\infty##). The Wikipedia article on polytropic processes states that the specific heat...
  19. P

    Heat transfer in polytropic process

    Homework Statement A piston/Cylinder arrangement of initial volume 0.025 m3 contains saturated water vapor at 180 degree Celsius. The steam now expand in a Polytropic process with exponent n=1 to a final pressure of 200 kpa while it does work against the piston. Determine the heat transfer...
  20. R

    Thermodynamics Polytropic Process Compressor

    I was revising for my course exam and encountered a question in my book (Applied Thermodynamics for Engineering Technologists, p 66 example 3.3) which stated that a compressor follows a polytropic process to compress air; I understood the calculation process which resulted in heat being...
  21. V

    Pressure-Time relation for polytropic thermodynamic process

    Dear Friends, I carried out an experiment of sudden release of oxygen (open nozzle) from an oxygen cylinder used for medical college and hospitals. I found that pressure drops quite rapidly and cylinder surface cools from outside such that water droplets accumulate on its surface. This...
  22. S

    Isentropic efficiency vs polytropic efficiency of a gas turbine

    My classmates and I are working on a senior design project where we optimize a baseline turbofan for supersonic cruise. We are a little confused about when to use polytropic vs isentropic efficiencies. I have read to begin with isentropic, however is there anyone who could explain a little more...
  23. I

    Polytropic process vs perfect gas eq

    The polytropic law states: (1) P1V1n = P2V2n The perfect gas equation states: PV = mRT --> P1V1/T1 = P2/V2/T2 If T1 = T2 then (2) P1V1 = P2V2 So, how can equation 1 and 2 both be true for the same gas? If the gas follows a polytropic process, where n ≠ 1, how can 2 be...
  24. S

    What is the Polytropic Exponent, n Value for a Singular Repeating Compressor?

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  25. LunaFly

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  26. N

    Entropy in polytropic processes

    Homework Statement I have question on entropy for which I have no idea about, please help me out... a) Change of entropy of a gas is given with usual notations by: s2-s1=cvln(T2/T1)+Rln(V2/V1) using this relationship, show that for a polytropic process, entropy change can be expressed as...
  27. M

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  28. J

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  29. M

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    Hi, something is a bit confusing in regards to polytropic processes.Can anyone explain why boundary work in closed system for compressor is calculated as W = ∫pdV and polytropic process after integration is generally W = -(p2V2 - p1V1)/(1-n)...(numbers behind p and V are subscripts)... When we...
  30. M

    Thermodynamics polytropic processes and work for them

    Hi, something is a bit confusing in regards to polytropic processes.Can anyone explain why boundary work in closed system for compressor is calculated as W = ∫pdV and polytropic process after integration is generally W = -(p2V2 - p1V1)/(1-n)...(numbers behind p and V are subscripts)... When we...
  31. J

    Equation of polytropic process as dS=f(n)

    Hej, basicaly what I have is a program that calculates states of the gas in Carnot cycle (Jet engine). Now my intention is to plot it in T-S diagram. To do that, knowing the states after an each component of engine, I need to evaluate a temperature as a function of Enthropy change knowing only...
  32. G

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  33. T

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    Homework Statement From a previous problem, we have found that the pressure inside the sun can be represented by a polytrope with index n=3. Does this mean that the sun contains relativistic degenerate matter, which is also described by a polytrope with index 3? Explain how a polytrope with...
  34. S

    Polytropic exponent, thermodynamics question

    Homework Statement Air is compressed to 6% of its initial volume in the cylinder of a diesel engine. In the process, its pressure increased from 1 bar to 41 bar. Calculate the polytropic exponent for this process and comment on the associated heat transfer. Homework Equations PV^λ...
  35. E

    Polytropic processes on a PV plot

    1 -> 2 : Isochoric heat addition 2 -> 3 : Polytropic expansion 3 -> 1 : Isobaric compression back to the initial state Sketch this cycle on a pressure-volume plot in relation to the saturation curve. Now, my question is, why is the polytropic process on the PV plot concave up and not...
  36. M

    Calculating pressure fromV1 to V2 with a polytropic exponent

    Homework Statement I have a bicycle pump where I need to calculate the pressure in a certain volume. No heat is lost during compression so this is a isentropic system initial volume is 0.3L final volume is 0.0195 Gas is air n=k Homework Equations I don't know, that's the problem...
  37. J

    Polytropic Processes: Reversible vs Irreversible

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  38. C

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    Hi I really need help figuring out this problem. A balloon behaves such that the pressure inside is proportional to the diameter squared. It contains 2 Kg of ammonia at 0 degrees celcius and 60% quality. The balloon and ammonia are now heated so that a final pressure of 600 kPa is reached...
  39. J

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    Homework Statement A gas is trapped in a cylinder-piston arrangement. The initial pressure and volume are 13,789.5 Pa and 0.02832 m^3. Determine the work(kj) assuming that the volume is increased to 0.08496 m^3 in a polytropic process with n=1. Homework Equations m_1-2=∫PdV from 1 to...
  40. S

    Otto cycle with polytropic compression and expansion (thermodynamics)

    Homework Statement attached as pdf (problem 1) (part b)Homework Equations w=p2v2-p1v1 / n-1 w=mR(T2-T1) / 1-nThe Attempt at a Solution I was able to determine the pressure and temperatures at all points, but to find the work i appear to need the volume, I also looked at w=h2-h1 but I am not...
  41. M

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  42. D

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    Helium gas initially at 2 bar, 200K undergoes a polytropic process, with n=k, to a final pressure of 14 bar. Determine the work and heat transfer for the process, each in kJ per kg of helium. Assume ideal gas behavior. Ok so I have the following: P1=200kPa T1=200K R_He=2.0769kJ/kg*K...
  43. C

    Polytropic Process Work & Heat Transfer Calculation

    Homework Statement A pistol-cylinder device contains 0.8kg of nitrogen initially at 100kPa and 27 degrees C. The nitrogen is compressed in a polytropic process during which PV^1.3 = constant until the volume is reduced by one half. Determine the work done and the heat transfer for this...
  44. J

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    definition wise i got the difference between these two efficiencies. but in practice how does these two differ? i was referring to this book: Jet propulsion: a simple guide to the aerodynamics and thermodynamic design ... By N. A. Cumpsty he has mentioned this: "using polytropic...
  45. R

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  46. S

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    Homework Statement "During some actual expansion and compression processes in piston-cylinder devices, the gases have been observed to satisfy the relationship PV^n=c where n and C are constants. Calculate the work done when a gas expands from 150kPa and .03 m^3 to a final volume of .2m^3 for...
  47. R

    Steam, Piston-cylinder system polytropic

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  48. J

    Polytropic efficiency vs isentropic efficiency?

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  49. V

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  50. G

    Polytropic Models: Solving Problem at Slide 5

    Hello, I am studing polytropes and I found something intersting here: http://astronomy.sussex.ac.uk/~pd48/Polytropes.ppt I got a problem at slide 5 where she says that the polytropic index n is equal to 0 for a homogenous gas sphere. I am not able to figure out why. From the polytropic...
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