Thermodynamics and Propulsion

... evidence^1.1

Alternatively, most thermodynamic principles and can be derived from kinetic theory.

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... applications^1.2

$p«p_{\textrm{crit}}$ , and $T>2 T_{\textrm{crit}}$ up to about $4p_{\textrm{crit}}$ , [VW, S & B: 3.4].

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... behavior^1.3

See Section 5.2 for the other laws and credit for this form.

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... substances^2.1

As an aside: The derivative $(\partial u/\partial T)_v$ represents the slope of a line of constant $v$ on a $u$ -$T$ plane.

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... terminology^2.2

Course Notes, ``Ideal Gases,'' Prof. Georg Gyarmathy, Swiss Federal Institute of Technology, Zurich.

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... hundred.^2.3

Adapted from Zemansky, M. W., and Dittman, R. H., ``Heat and Thermodynamics,'' Sixth Edition, McGraw-Hill book company, 1981.

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... substances.^2.4

Adapted from ``Engineering Thermodynamics,'' Reynolds, W. C., and Perkins, H. C., McGraw-Hill Publishers.

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... number^2.5

The Mach number, $M$ , is the ratio of the flow speed, $c$ , to the speed of sound, $a$ . You will learn more about this quantity in fluids, but it is interesting to see that $M^2$ measures the ratio of the kinetic energy of the gas to its thermal energy.

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... neglected)^3.1

In general this is a good assumption since in typical combustion applications the fuel accounts for only about 5% of the mass of the working fluid.

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... state^3.2

This fact is often useful for solving thermodynamic cycles in different ways. For instance, in this example we could sum the work terms all around the cycle. Instead we will consider the difference between the heat added to the cycle in process $b$ -$c$ , and the heat rejected by the cycle in process $d$ -$a$ .

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... boundaries^4.1

Indeed, some ability to do work was lost, for we could have put a piston in the volume and allowed the expansion of the gas to do work to raise a weight.

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... magnitude^4.2

Note that without our external work, the gas would not move itself back into $V_1$ , even though such a spontaneous reversal would be compatible with the First Law.

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... explicit.^5.1

From notes of Professor F. E. C. Culick, California Institute of Technology (with minor changes).

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... irreversibility^6.1

This and the following paragraph are excerpted with minor modifications from A Course in Thermodynamics, Volume I, by J. Kestin, Hemisphere Press (1979).

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... surroundings)^6.2

In the above equation, and in the arguments that follow, the quantities $Q_\textrm{rev}$ and $W_\textrm{rev}$ are both regarded as positive for work done by the surroundings and heat given to the surroundings. Although this is not in accord with the convention we have been using, it seems to me, after writing the notes in both ways, that doing this gives easier access to the ideas. I would be interested in your comments on whether this perception is correct.

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... Perkins^7.1

Reynolds, W.C., and Perkins, H.C., Engineering Thermodynamics, McGraw-Hill Book Co., 1977.

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... out^8.1

These assumptions are reasonable for temperatures well below the critical temperature.

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...)^11.1

Here we can switch from $F$ to the more mnemonic $T$ because temperature will not play a significant role in our analysis.

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... propulsive^13.1

The transmission efficiency represents the ratio between compressor and turbine power, which is less than unity due to parasitic frictional effects. As with the combustion efficiency, however, this is very close to one and the horizontal axis can thus be regarded essentially as propulsive efficiency.

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... negligible^18.1

Note: We don't need to make this assumption, and if we were looking at the problem in detail we would solve it numerically and not worry about whether an analytic solution existed. In the present case, developing the analytic solution is useful in presenting the structure of the solution as well as the numbers, so we resort to the mild fiction of no heat transfer at the fin end. We need to assess, after all is said and done, whether this is appropriate or not.

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