Constant cp Cv Ideal gas const.specific heat: 0 s(T2 U2)--s(Ti,v1)=coIn+R In T V ->0 T2 sP-Tp）=Gl P2 pi Ideal gas const.specific heat isentropic: 0 (k-1)/k T2 P2 巧刀 (s=S2,constant k) 0= kR Pi Cp= - k-I T2 T (s1=S2,constant k) R 0=colr 02 +R In- D T Ui c=k-1 (S1 S2,constant k) P 上游气通大粤 April 27,2018 6 SHANGHAI JIAO TONG UNIVERSITY
April 27, 2018 6 + Constant cp , cv Ideal gas + const. specific heat: Ideal gas + const. specific heat + isentropic: 0 0
Polytropic process (S1=S2.constant k) 。pwk= constant a polytropic process of an ideal gas with constant k is an isentropic process. P n=-1 n =k n=±oo v=constant n=-1 n=0 n=0 p constant n=1 T=constant constant n=1 n=士o n=k S 上游充通大 April 27,2018 7 SHANGHAI JIAO TONG UNIVERSITY
April 27, 2018 7 Polytropic process a polytropic process of an ideal gas with constant k is an isentropic process
Example 35.1 air leaking from a tank Known:rigid,well insulated. m1=5 kg air,p1 =5bar,T1=500 K. System boundary slow leak until p2 1bar Slow leak Find: m2,T2 Assumptions: Mass initially 1.the closed system is the mass initially in the in the tank that Mass initially in the remains in the tank tank that remains in the tank. tank that escapes 2.There is no significant heat transfer between the system and its surroundings. Initial condition of tank 3.Irreversibilities within the tank can be ignored as the air slowly escapes. 4.The air is modeled as an ideal gas. initial amount of mass within the tank m= (R/M)T mass initially in the tank that remains in the tank 1m2 (R/M)T2 上游充通大 April 27,2018 8 SHANGHAI JIAO TONG UNIVERSITY
April 27, 2018 8 Example 35.1 air leaking from a tank Known: rigid, well insulated. m1=5 kg air, p1 =5bar, T1=500 K. slow leak until p2 = 1bar Find: m2 , T2 Assumptions: 1. the closed system is the mass initially in the tank that remains in the tank. 2. There is no significant heat transfer between the system and its surroundings. 3. Irreversibilities within the tank can be ignored as the air slowly escapes. 4. The air is modeled as an ideal gas. mass initially in the tank that remains in the tank initial amount of mass within the tank ? ?