Recall Gibbs eqn. ds. Using h version. for ideal gas. integrate AE3450. for ideal gas. integrate s. s(t,p) behavior? AE3450. T p.

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1 Enti Shl f Aeae State Engineeing Eqn. Ideal Gae du eall Gibb eqn. d f ideal ga d integate d d d Ideal Ga Enty State elatin - Cyight 03 by Jey M. Seitzman. All ight eeed. d d d d d ln d ln Enti Shl f Aeae State Engineeing Eqn. Ideal Gae Uing h ein f ideal ga integate dh d d d d d d d d ln (,) behai? Ideal Ga Enty State elatin - Cyight 03 by Jey M. Seitzman. All ight eeed. deendene, deendene, due t due t and deendene i eaable!! al tue f (,)

2 Enti Shl f Aeae State Engineeing Eqn. Ideal Gae S an geneally wite with e.g., with d ef d ef tyially 0 K ( ) ln an alulate and/ find in table eay t alulate Ideal Ga Enty State elatin -3 Cyight 03 by Jey M. Seitzman. All ight eeed. Simlifying f =nt. CPG Shl f Aeae Engineeing (+Ideal) Equatin nmalizing d ln ln ln ln ln (,) ln ln enty me enitie t hange ln ln d ln ln ln (,) Ideal Ga Enty State elatin -4 Cyight 03 by Jey M. Seitzman. All ight eeed.

3 Shl f Aeae Engineeing Ai Examle Gien: Ai 7 C, atm; late ame meed t 37 C, 50 atm Find: Enty hange f g and nn-g ae Aume: tg Ideal Ga Enty State elatin -5 Cyight 03 by Jey M. Seitzman. All ight eeed. Ideal Ga Enty State elatin -6 Cyight 03 by Jey M. Seitzman. All ight eeed. Shl f Aeae Engineeing Ai Examle: Slutin 0.46 kj kgk 7C atm Analyi (g): State Eqn. ln ln need alue f, 87 J kgk mut ue ablute ~.4 3.5, K J 600K ln ln kgk 300K kj kgk fat f 50 ineae in nly abut twie the effet f ineae in 37C 50 atm 3

4 600K 300K Analyi (nn-g): State Eqn. Ideal Ga Enty State elatin -7 Cyight 03 by Jey M. Seitzman. All ight eeed. Shl f Aeae Engineeing Ai Examle: Slutin ln fm able D. kj kj kgk kgk wa kj kgk if ithemal? < 0??? kj 0.45 kgk 300K atm <% diffeene in () tem f g alulatin e K 600K 50 atm tem ame, een if nt g had t hae been led duing e Ideal Ga Enty State elatin -8 Cyight 03 by Jey M. Seitzman. All ight eeed. Shl f Aeae Engineeing - Diagam Often dawing a e n a - tate diagam will be ey helful t undetanding the e ithemal e? ienti e? ibai e? what d line f ntant lk like? an hw f tg le ineae with, lwe eue line? Nte: line diege t the ight Cling Heating Ie. 3 > > 3 4

5 5 Ideal Ga Enty State elatin -9 Shl f Aeae Engineeing Cyight 03 by Jey M. Seitzman. All ight eeed. Ienti elatin - PG What an we ay f =0? F tg ln 0 d ln d d ien e e e ()/ aailable in bk table a ienti ienti imilaly Ideal Ga Enty State elatin -0 Shl f Aeae Engineeing Cyight 03 by Jey M. Seitzman. All ight eeed. Ienti elatin PG and CPG F ien. & g uing = ln ln 0 ien ienti e ien nt ine > will need thi late

6 Shl f Aeae Engineeing Autmbile Engine Examle Gien: Ai meed in aut engine ylinde with mein ati f 0 (=V /V ), a tyial alue Find:, =300K = atm Aume: tg, g (=.4) mein fat enugh that n heat tanfe t ylinde wall BU lw enugh t be eeible Ideal Ga Enty State elatin - Cyight 03 by Jey M. Seitzman. All ight eeed. Shl f Aeae Engineeing Aut Engine Examle: Slutin Analyi: Ma Cne. nd Law e+adiab ienti m m V V m m V V =754K =5atm =300K = atm Ideal Ga Enty State elatin - Cyight 03 by Jey M. Seitzman. All ight eeed. 6

7 Shl f Aeae Engineeing Aut Engine Examle: Slutin What if dn t aume g: V till hae V Ue able D. (K) C kj/kgk Ideal Ga Enty State elatin -3 Cyight 03 by Jey M. Seitzman. All ight eeed. K =300K = atm ~ 730K 0 ien. 754 K atm.38 ien. 5 atm Shl f Aeae Engineeing Stagnatin Examle Gien: 300 K, atm, 700 m/ =300K = atm =700 m/ Find: Peue ( ) if flw i lwed eeibly and adiabatially t ze elity (tagnatin eue) Aume: tg, g (=.4) and n extenal wk Ideal Ga Enty State elatin -4 Cyight 03 by Jey M. Seitzman. All ight eeed. 7

8 Shl f Aeae Engineeing Stagnatin Examle: Slutin Analyi: t =300K Law aleady hwed = atm if Q=0, W=0 h =700 m/ h and if g tagnatin temeatue nd Law e+adiabienti kgk 87 J ~ Ideal Ga Enty State elatin -5 Cyight 03 by Jey M. Seitzman. All ight eeed m 300 J =544K =8.0atm.8 kg What if e ie.? 8

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