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Thermodynamics Notes 17

# Thermodynamics Notes 17 - ME 311 FALL 2007 CHAPTER...

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ME 311 THERMODYNAMICS S. Masutani FALL 2007 CHAPTER 6 (continued) Having derived relationships for changes in entropy of two idealized substances (ideal gases and incompressible substances), we next consider their application in processes or events in which the entropy of the system or the universe is constant, i.e., in isentropic processes where s 2 = s 1 . This corresponds to a reversible (or internally reversible) process. For a SCS (or an ideal gas), the state of the system is determined by a single pair of independent properties. Thus, if a process is idealized as isentropic going from state 1 to state 2, and if s 1 is known, then a single additional property, e.g., T 2 , p 2 , h 2 , will fix state 2: T s 1 2 P 1 P 2 For an ideal gas undergoing an isentropic process between states 1 and 2: = = = = = = R T s R T s R T s T s p p p p R T s T s p p R T s T s p p R T s T s s s o o o o o o o o o o ) ( exp ) ( exp ) ( ) ( exp ln ) ( ) ( ln ) ( ) ( ln ) ( ) ( 0 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 The quantity ) ( ) ( exp ) ( T f R T s T P o r = is called the relative pressure and is tabulated for different gases. Thus, for an ideal gas undergoing an isentropic process: 1 2 1 2 r r P P p p = 1

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ME 311 THERMODYNAMICS S. Masutani FALL 2007 For an ideal gas, the equation of state is pv =RT It follows that the ratio of the specific volumes at the two states 1 and 2 (for the gas undergoing an isentropic process) can be expressed as 1 1 2 2 1 1 2 2 1 1 2 2 1 2 RT P P RT RT p p RT p RT p RT v v r r = = = The quantity ) ( ) ( T v T P RT r r is called the relative volume and, like the relative pressure, Pr, is also tabulated. Summarizing For an ideal gas undergoing an isentropic process : 1 2 1 2 1 2 1 2 r r r r v v v v P P p p = = If, in addition, Cv(T) = constant and Cp(T) = constant (i.e., a calorically perfect gas), then we can apply the relationships = + = = 1 2 1 2 1 2 1 2 1 2 ln ln ln ln 0 p p R T T C v v R T T C s s p v We can utilize the definition γ (or k) v p C C
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Thermodynamics Notes 17 - ME 311 FALL 2007 CHAPTER...

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