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Unformatted text preview: AA 311 Lecture 10: Elementary Thermodynamics Reading: [1] Chapters 4.5. Highspeed flow of gas is also a highenergy flow. The kinetic energy of the fluid elements in a high speed flow is large, and must be taken into account. When highspeed flow is slowed down, the reduction in kinetic energy may result in a substantial increase in temperature and density. Hence highspeed flows, compressibility, and vast energy changes are all related. To study highspeed aerodynamics and compressible flows, one first needs to examine some of the fundamentals of the energy changes in a gas, and the consequent changes in pressure and temperature. First, recall the first law of thermodynamics. We will study a system of gas of unit mass that has a boundary, A , takes up some volume, v , and is able to exchange energy with its surroundings. Such a system is depicted in Figure 1. The internal energy of this system will be denoted as e . An incremental Figure 1: System of unit mass of gas. change to the internal energy is denoted de . There are two ways the systems internal energy can be increased: Heat is added to the system across the boundary: q . Work is done on the system: w . The first law of thermodynamics states that an increase in a systems internal energy can come from either or both of two sources only: 1) heat added to the system; 2) work done on the system: de = q + w. (1) Consider the system shown in Figure 2. Suppose work is done on the system, by effect of which an elemental surface area dA is pushed in an incremental distance s . By definition, work is force times distance, hence W = pdAs. The total work done on the system is the sum of all the work done over the boundary, or in terms of calculus w = Z A psdA. Suppose that pressure, p , is constant, then w = p Z A sdA. 1 Figure 2: System of unit mass of gas. The integral above is geometrically the change in volume of unit mass of gas inside the system (see Figure 2, right), hence Z A sdA = dv. Using this relation, we can write the work done on the system in terms of pressure and specific volume: w = pdv. (2) Substituting equation 2 into (1), we get an alternative form of the first law q = de + pdv....
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This document was uploaded on 02/05/2012.
 Fall '09

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