Heat and Work of a POLYTROPIC Process in 3 Minutes!

Polytropic Processes
Isobaric, Isothermal, Isochoric, Adiabatic
Ideal Gas Equation
Work Equations for Polytropic Process

Example 3: coming August 2022

Main Lecture:
13. Polytropic Process Work:

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Other Thermodynamics Lectures:

19. Transient Systems:
28. Otto Cycle:
29. Standard Diesel Cycle:
30. Rankine Cycle:
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Other Engineering Courses (Playlists):

[lglb]

I had to make some of the same ‘mental re-adjustments’ as some others; as we were used to ‘n = moles’ equations and a goofy n (~eta) for polytropic index. In that world, n moles are used, but in others like this one, some use mass and modify other units like R and cv. I, like another commenter, first converted everything out of mass and back into moles, etc., to plug into my familiar equations. Either way, I was getting different answers for the last step Q (aside from all the rounding details). I tore it down to the core, and found the issue, but don’t know how to resolve it.

Essentially… to derive the polytropic equation for W = delta(PV) / (1-eta) you essentially end up substituting the Isentropic gamma (or kappa k in some disciplines) with the polytropic eta (n*) which came from cv=R/(1-eta) vs. cv=R/(1-gamma), yet in the last step of Q =, you look up cv? In other words, behind the scenes of Q = W + delta(U), the work equation is relying on a cv built from cv=R/(1-eta), and the total energy equation is relying on a different cv built from cv=R/(1-gamma), plus that’s a table-looked-up value which certainly uses the gamma cv and actually lists gamma (kappa) right there as 1.399, so definitely not an eta (n*) based cv (like 1.3 here for this example problem)

So for polytropic processes, does cv=R/(1-gamma) or cv=R/(1-eta) because gamma does not equal eta (1.399 ≠ 1.3). So different cv’s are being used for W and delta(U) in determining Q. And I confirmed that by using the different cv’s in my go-to total energy equation delta(U) = n*cv*delta(T). I get the same answer for Q as in the video only when using the gamma-based cv for energy and the eta-based cv for the work, Q = W[eta cv] + delta(U)[gamma cv]. Specifically, I have to use the eta cv in the work equation (as it is derived that way) but use the gamma cv in delta(U) (as this sample problem does and even looks it up). So… using two different values for cv in the same equations determining Q here?

[AnushaYadav_Indian]

Really nice explanation!! Helpful for JEE preparation!!

[chelseodende]

Sir, there, during the numerical, u used mass(m) instead of number of mols(n), I think u should first find the 'n' by the mass and molecular weight so then u can obtain the value of 'n' and replace in the formula

[elguapochulo]

why Delta U= m*cv( T2-T1) and not Delta U =cv(T2-T1). why is mass included