The system mass is constant (m=m, +m,= constant so that for any changes We can define the quantity dme dmo dm. =-dm,= mass transferred from liquid to vapor In terms of dm f the volume change of the system is The work done is given by dw= pdy The change in internal energy, AU, can be found as follows. The internal energy of the system can be expressed in terms of the mass in each phase and the specific internal energy(internal energy per unit mass, u) of the phase as U=ume.m d0=urdm +u, dm Note that the specific internal energy can be expressed in a similar way as the specific volume in terms of the quality and the specific enthalpy of each phase X:a2+(1-X) Writing the first law for this process do=du+ dm ur)dme+p(vg-v,a Py Pve ldr mfg h -he ldm The heat needed for the transfer of mass is proportional to the difference in specific enthalpy between vapor and liquid. The pressure and temperature are constant, so that the specific internal energy and the specific enthalpy for the liquid phase and the gas phase are also constant. For a finite change in mass from liquid to vapor, m fe, therefore, the quantity of heat needed is 0=(n-h ) mg-AH (enthalpy change) 2B-62B-6 The system mass is constant ( mm m =+= f g constant) so that for any changes dm dm dm == +f g 0 . We can define the quantity dmfg dm dm dm fg = =g f - = mass transferred from liquid to vapor. In terms of dmfg the volume change of the system is dV v v dm = − ( ) g f fg . The work done is given by dW = PdV = − P v v dm ( ) g f fg . The change in internal energy, ∆U , can be found as follows. The internal energy of the system can be expressed in terms of the mass in each phase and the specific internal energy (internal energy per unit mass, u) of the phase as, U um um = + f f g g dU u dm u dm u u dm = + =− f f gg g ( )f fg . Note that the specific internal energy can be expressed in a similar way as the specific volume in terms of the quality and the specific enthalpy of each phase: u Xu X u =⋅ +− ⋅ g f ( ) 1 Writing the first law for this process: dQ = dU + dW = − ( ) u u dm P v g f fg + − ( ) g v dm f fg . = + [ ] ( ) u Pv u g g − + ( ) f f fg Pv dm = − ( ) h h dm g f fg. The heat needed for the transfer of mass is proportional to the difference in specific enthalpy between vapor and liquid. The pressure and temperature are constant, so that the specific internal energy and the specific enthalpy for the liquid phase and the gas phase are also constant. For a finite change in mass from liquid to vapor, mfg, therefore, the quantity of heat needed is Q h hm H = − ( ) g f fg = ∆ (enthalpy change)