5.2.4 Inner energy exergyFor closed systemFrom initial state (p, v, s,u) to final state (po, Vo, So,uo)0
For closed system From initial state ( , , , ) p v s u 0 0 0 0 to final state ( , , , ) p v s u 5.2.4 Inner energy exergy
ForABOq=uo-u+wq=qA-B +qB=0 =0+T(S -S)w=(u-uo)-T,(s-So)The dead work to resist environmentPo(vo -v)Themaximum worke, =(u-uo)-T(s-So)+po(v -vo)
For A→B→O 0 q u u w = − + 0 0 0 ( ) A B B O q q q T s s = + = + − → →0 0 0 w u u T s s = − − − ( ) ( ) The dead work to resist environment 0 0 p v v ( ) − The maximum work 0 0 0 0 0 ( ) ( ) ( ) x e u u T s s p v v = − − − + −
Form kg substanceE, =(U-U.)-T(S- So)+ po(V -V)The maximum available work=exi -exz =(u -u,)-T(si -s2)+ po(vi -v2)(Wi-2 )max
For m kg substance 0 0 0 0 0 ( ) ( ) ( ) E U U T S S p V V x = − − − + − The maximum available work 1 2 max 1 2 1 2 0 1 2 0 1 2 ( ) ( ) ( ) ( ) w e e u u T s s p v v − x x = − = − − − + −
TT1Si constantT.=constantQ力234Exergy in p -v diagram
Exergy in diagram p v −
ExamplePlease calculate the inner energy exergyof air in the state of 1MPa and 50C. Theenvironmental pressureispo=0.1MPa,thetemperature is T=25C and the specificheatisc=0.716kJ/(kg-K)
Please calculate the inner energy exergy of air in the state of 1MPa and 50℃. The environmental pressure is p0=0.1MPa，the temperature is T0=25℃ and the specific heat is cv =0.716kJ/(kg·K)。 Example