Physics Help Forum Need assitance re: Internal energy calculations on Polytropic expansion

 Dec 3rd 2016, 06:45 PM #1 Junior Member   Join Date: Dec 2016 Posts: 2 Need assitance re: Internal energy calculations on Polytropic expansion Hi everyone, I'm having an issue with a question I'm trying to solve. Here is the question: A gas with an initial pressure of 800Kpa, 0.02m3 expands following a polytropic process. The final conditions are 350Kpa, 0.042m3. Find the following: a) Index of expansion b) Work done c) Change in Internal Energy d) Heat transfer I'm stuck on c). If someone could guide me through it would be of help. Answers so far: a) n = 1.11 using P1/P2 = (V2/V1)^n b) 11.82KJ using P1V1-P2V2/n-1 Why I'm stuck: During my studies I've found internal energy to be only tied to temperature. What am I missing? Thanks gentlemen.
 Dec 4th 2016, 03:50 PM #2 Senior Member   Join Date: Jun 2010 Location: NC Posts: 361 The idenity of the gas and its critical properties are not stated. The mass is not known. The idea "Polytropic" is most commonly used with the system substance assumed to be an ideal gas. In general internal energy of a simple compressible substance has dependence: u = u(T,v). In actuality, as space expands, pressure diminishes or temperature rises - or in combination... the internal energy comes to depend on temperature only u = u(T). To understand, one must sketch the event on p-v coordinates. Work is the area under the curve. The change of internal energy is cv(T2-T1). Put the work and the IE change into the energy equation. Good Luck Blowgun Hunter | THERMO Spoken Here! topsquark likes this.
 Dec 4th 2016, 03:57 PM #3 Senior Member   Join Date: Jun 2010 Location: NC Posts: 361 polytropic - say what? I now recall I sumarized the classical idea "polytropic" at my site. Here is my perspective of "what it is!" C:\Users\Jim\a_ROOT\wp\03_tsh\C6100_3.20_polytropi c\polytropic.html Good Luck again... JP
Dec 4th 2016, 04:05 PM   #4
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 Originally Posted by THERMO Spoken Here The idenity of the gas and its critical properties are not stated. The mass is not known. The idea "Polytropic" is most commonly used with the system substance assumed to be an ideal gas. In general internal energy of a simple compressible substance has dependence: u = u(T,v). In actuality, as space expands, pressure diminishes or temperature rises - or in combination... the internal energy comes to depend on temperature only u = u(T). To understand, one must sketch the event on p-v coordinates. Work is the area under the curve. The change of internal energy is cv(T2-T1). Put the work and the IE change into the energy equation. Good Luck Blowgun Hunter | THERMO Spoken Here!
Thanks for the response. Here is my issue: without a Cv I can't solve.

I can use the P-V-T relationships to sub out DeltaT but can't solve. I can create a Cv using R: 8.314 but can I substitute gamma for my N index?

I still don't see it using the fundamental equation. Cv is my hold up.

 Dec 4th 2016, 06:11 PM #5 Senior Member   Join Date: Jun 2010 Location: NC Posts: 361 You are correct - I over-looked the cv necessity. The problem statement is incomplete. How would one know so much without knowing the gas species? No answer possible without a guess. So you can say: If monatomic cv = 3/2(R/M) and... or if diatomic cv = 5/2(R/M) and ... Actually you don't know the molecular species so ???????

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